Cremona's table of elliptic curves

120768 = 2⁶ · 3 · 17 · 37

Class	r	Atkin-Lehner	Eigenvalues
120768a (1 curve)	1	2+ 3+ 17+ 37+	2+ 3+  0 -3 -2 -5 17+ -8
Curve Equation t Generators 120768a1 [0,-1,0,113087,26924353] 1 [-29:4860:1]
120768b (1 curve)	1	2+ 3+ 17+ 37+	2+ 3+ -1  3  1  2 17+  3
Curve Equation t Generators 120768b1 [0,-1,0,-20321,1121889] 1 [83:12:1]
120768c (2 curves)	1	2+ 3+ 17+ 37+	2+ 3+  2  0  0  4 17+  6
Curve Equation t Generators 120768c1 [0,-1,0,-40417,-6521375] 2 [964529839406301:6476922507214880:3482088074893] 120768c2 [0,-1,0,-826497,-288724095] 2 [13735255:178668080:12167]
120768d (2 curves)	1	2+ 3+ 17+ 37+	2+ 3+ -3 -1 -3  4 17+  1
Curve Equation t Generators 120768d1 [0,-1,0,4863,-29439] 1 [15:216:1] 120768d2 [0,-1,0,-75777,-8335359] 1 [1167:38616:1]
120768e (1 curve)	0	2+ 3+ 17+ 37-	2+ 3+ -1  2  1  3 17+  5
Curve Equation t 120768e1 [0,-1,0,-721301,236029389] 1
120768f (1 curve)	0	2+ 3+ 17+ 37-	2+ 3+ -1  2  4 -3 17+ -7
Curve Equation t 120768f1 [0,-1,0,479,25249] 1
120768g (4 curves)	0	2+ 3+ 17+ 37-	2+ 3+ -2  0  4  6 17+ -4
Curve Equation t 120768g1 [0,-1,0,596,-4466] 2 120768g2 [0,-1,0,-3049,-37271] 4 120768g3 [0,-1,0,-21409,1185505] 2 120768g4 [0,-1,0,-43009,-3417887] 2
120768h (1 curve)	2	2+ 3+ 17+ 37-	2+ 3+ -4 -1 -6  5 17+  0
Curve Equation t Generators 120768h1 [0,-1,0,-1665,26721] 1 [21:-24:1]&[5:136:1]
120768i (1 curve)	0	2+ 3+ 17- 37+	2+ 3+  0  5  2  5 17- -8
Curve Equation t 120768i1 [0,-1,0,607,-48351] 1
120768j (2 curves)	2	2+ 3+ 17- 37+	2+ 3+ -3  2 -3 -5 17-  7
Curve Equation t Generators 120768j1 [0,-1,0,203,4999] 1 [42:-629:8]&[42:293:1] 120768j2 [0,-1,0,-1837,-141881] 1 [114:1057:1]&[10026:354571:8]
120768k (1 curve)	1	2+ 3+ 17- 37-	2+ 3+  1 -1  1 -2 17-  5
Curve Equation t Generators 120768k1 [0,-1,0,-89505,-14083551] 1 [2511:124848:1]
120768l (1 curve)	1	2+ 3+ 17- 37-	2+ 3+  1 -2  1 -5 17- -1
Curve Equation t Generators 120768l1 [0,-1,0,-3000925,-2009196377] 1 [295770:8035067:125]
120768m (1 curve)	1	2+ 3+ 17- 37-	2+ 3+  1 -5  1 -2 17- -7
Curve Equation t Generators 120768m1 [0,-1,0,-43745,3735393] 1 [-1:1944:1]
120768n (1 curve)	1	2+ 3+ 17- 37-	2+ 3+ -1  1  1  4 17-  5
Curve Equation t Generators 120768n1 [0,-1,0,799,65889] 1 [32:351:1]
120768o (1 curve)	1	2+ 3+ 17- 37-	2+ 3+ -1 -1  1  0 17- -1
Curve Equation t Generators 120768o1 [0,-1,0,-2055521,1137929697] 1 [1139:16524:1]
120768p (1 curve)	1	2+ 3+ 17- 37-	2+ 3+ -1  3  1 -4 17-  5
Curve Equation t Generators 120768p1 [0,-1,0,1679,43537] 1 [21:-296:1]
120768q (1 curve)	1	2+ 3+ 17- 37-	2+ 3+ -1 -3  5  0 17-  5
Curve Equation t Generators 120768q1 [0,-1,0,-3316,74614] 1 [266:27:8]
120768r (1 curve)	1	2+ 3+ 17- 37-	2+ 3+ -1  5 -5  0 17- -1
Curve Equation t Generators 120768r1 [0,-1,0,-9314321,-10942219983] 1 [4429:186184:1]
120768s (4 curves)	1	2+ 3+ 17- 37-	2+ 3+ -2  4  4 -2 17-  8
Curve Equation t Generators 120768s1 [0,-1,0,1151,66433] 2 [439890:9246587:1000] 120768s2 [0,-1,0,-19329,971649] 4 [1763:73780:1] 120768s3 [0,-1,0,-62849,-4903551] 2 [-95:448:1] 120768s4 [0,-1,0,-303489,64452993] 4 [53402429:2164164940:29791]
120768t (1 curve)	1	2+ 3+ 17- 37-	2+ 3+  3  0  3  7 17- -5
Curve Equation t Generators 120768t1 [0,-1,0,-719,8157] 1 [4:73:1]
120768u (1 curve)	1	2+ 3+ 17- 37-	2+ 3+  3 -3 -3  4 17-  1
Curve Equation t Generators 120768u1 [0,-1,0,476,-7514] 1 [170:867:8]
120768v (1 curve)	1	2+ 3+ 17- 37-	2+ 3+ -3  2  0 -1 17-  3
Curve Equation t Generators 120768v1 [0,-1,0,63,2241] 1 [1:48:1]
120768w (1 curve)	0	2+ 3- 17+ 37+	2+ 3-  0  1  6 -1 17+  0
Curve Equation t 120768w1 [0,1,0,-193,5279] 1
120768x (1 curve)	2	2+ 3- 17+ 37+	2+ 3-  1 -1 -3 -4 17+ -1
Curve Equation t Generators 120768x1 [0,1,0,-465,3951] 1 [-25:24:1]&[15:24:1]
120768y (1 curve)	0	2+ 3- 17+ 37+	2+ 3-  1  2  0  5 17+  5
Curve Equation t 120768y1 [0,1,0,-4385,-404673] 1
120768z (1 curve)	0	2+ 3- 17+ 37+	2+ 3-  1 -3 -5  0 17+ -5
Curve Equation t 120768z1 [0,1,0,1187935,-2741072193] 1
120768ba (1 curve)	0	2+ 3- 17+ 37+	2+ 3-  1  5  3  0 17+ -1
Curve Equation t 120768ba1 [0,1,0,-65,927] 1
120768bb (1 curve)	0	2+ 3- 17+ 37+	2+ 3-  1 -5  3  0 17+  5
Curve Equation t 120768bb1 [0,1,0,14495,872447] 1
120768bc (1 curve)	0	2+ 3- 17+ 37+	2+ 3-  3 -3 -5  6 17+  5
Curve Equation t 120768bc1 [0,1,0,-4929,-337761] 1
120768bd (1 curve)	0	2+ 3- 17+ 37+	2+ 3- -3  1  3 -4 17+  3
Curve Equation t 120768bd1 [0,1,0,-101217,-12428289] 1
120768be (1 curve)	0	2+ 3- 17+ 37+	2+ 3- -3 -2  0 -1 17+  3
Curve Equation t 120768be1 [0,1,0,-78773537,401518925631] 1
120768bf (1 curve)	0	2+ 3- 17+ 37+	2+ 3- -3  3 -5  4 17+ -7
Curve Equation t 120768bf1 [0,1,0,-9781857,-11779682049] 1
120768bg (1 curve)	2	2+ 3- 17+ 37+	2+ 3- -3 -3 -5  4 17+  5
Curve Equation t Generators 120768bg1 [0,1,0,-1937,34479] 1 [-41:216:1]&[31:72:1]
120768bh (1 curve)	1	2+ 3- 17+ 37-	2+ 3-  0  3  2  1 17+ -4
Curve Equation t Generators 120768bh1 [0,1,0,-439713,501729471] 1 [-285:24576:1]
120768bi (4 curves)	1	2+ 3- 17+ 37-	2+ 3- -2  0 -4  6 17+  4
Curve Equation t Generators 120768bi1 [0,1,0,596,4466] 2 [317:5670:1] 120768bi2 [0,1,0,-3049,37271] 4 [-55:204:1] 120768bi3 [0,1,0,-21409,-1185505] 2 [-91:132:1] 120768bi4 [0,1,0,-43009,3417887] 2 [122:39:1]
120768bj (1 curve)	1	2+ 3- 17+ 37-	2+ 3-  3 -3  5 -2 17+ -7
Curve Equation t Generators 120768bj1 [0,1,0,111,-81] 1 [15:72:1]
120768bk (1 curve)	1	2+ 3- 17+ 37-	2+ 3- -4  1  6  5 17+  0
Curve Equation t Generators 120768bk1 [0,1,0,-1665,-26721] 1 [99:888:1]
120768bl (1 curve)	1	2+ 3- 17- 37+	2+ 3-  1 -3  1  6 17-  7
Curve Equation t Generators 120768bl1 [0,1,0,-4305,128367] 1 [-9:408:1]
120768bm (1 curve)	0	2+ 3- 17- 37-	2+ 3-  0  3  6 -1 17-  4
Curve Equation t 120768bm1 [0,1,0,-713473,472646495] 1
120768bn (1 curve)	0	2+ 3- 17- 37-	2+ 3-  1 -2 -5 -1 17-  1
Curve Equation t 120768bn1 [0,1,0,-5,-1629] 1
120768bo (1 curve)	0	2+ 3- 17- 37-	2+ 3- -1  3 -5  0 17- -5
Curve Equation t 120768bo1 [0,1,0,-3316,-74614] 1
120768bp (4 curves)	0	2+ 3- 17- 37-	2+ 3- -2  4  4  2 17-  4
Curve Equation t 120768bp1 [0,1,0,-2513489,1532944335] 2 120768bp2 [0,1,0,-2513569,1532841791] 4 120768bp3 [0,1,0,-2294529,1811154015] 4 120768bp4 [0,1,0,-2733889,1247968031] 2
120768bq (1 curve)	0	2+ 3- 17- 37-	2+ 3-  3  0 -3  7 17-  5
Curve Equation t 120768bq1 [0,1,0,-719,-8157] 1
120768br (1 curve)	0	2+ 3- 17- 37-	2+ 3-  3 -1  3  4 17-  7
Curve Equation t 120768br1 [0,1,0,-1089,13599] 1
120768bs (1 curve)	0	2+ 3- 17- 37-	2+ 3-  3  3  3  4 17- -1
Curve Equation t 120768bs1 [0,1,0,476,7514] 1
120768bt (1 curve)	0	2+ 3- 17- 37-	2+ 3-  3 -3 -1 -4 17- -3
Curve Equation t 120768bt1 [0,1,0,260031,39573279] 1
120768bu (1 curve)	0	2+ 3- 17- 37-	2+ 3- -3 -3  3  2 17-  7
Curve Equation t 120768bu1 [0,1,0,63,-3681] 1
120768bv (1 curve)	2	2- 3+ 17+ 37+	2- 3+  0 -1 -6 -1 17+  0
Curve Equation t Generators 120768bv1 [0,-1,0,-193,-5279] 1 [37:-192:1]&[55:384:1]
120768bw (1 curve)	0	2- 3+ 17+ 37+	2- 3+  1  1  3  4 17+ -3
Curve Equation t 120768bw1 [0,-1,0,120,558] 1
120768bx (1 curve)	0	2- 3+ 17+ 37+	2- 3+  1  1  3 -4 17+  1
Curve Equation t 120768bx1 [0,-1,0,-465,-3951] 1
120768by (1 curve)	0	2- 3+ 17+ 37+	2- 3+  1  2  0 -7 17+  3
Curve Equation t 120768by1 [0,-1,0,-4385,-110367] 1
120768bz (1 curve)	0	2- 3+ 17+ 37+	2- 3+  1 -2  0  5 17+ -5
Curve Equation t 120768bz1 [0,-1,0,-4385,404673] 1
120768ca (1 curve)	0	2- 3+ 17+ 37+	2- 3+  1  3  5  0 17+  5
Curve Equation t 120768ca1 [0,-1,0,1187935,2741072193] 1
120768cb (1 curve)	0	2- 3+ 17+ 37+	2- 3+  1 -4  3 -1 17+ -3
Curve Equation t 120768cb1 [0,-1,0,56407565,690445068733] 1
120768cc (1 curve)	0	2- 3+ 17+ 37+	2- 3+  1  5 -3  0 17+ -5
Curve Equation t 120768cc1 [0,-1,0,14495,-872447] 1
120768cd (1 curve)	0	2- 3+ 17+ 37+	2- 3+  1 -5  1  4 17+  7
Curve Equation t 120768cd1 [0,-1,0,2840,-25826] 1
120768ce (1 curve)	2	2- 3+ 17+ 37+	2- 3+  1 -5 -3  0 17+  1
Curve Equation t Generators 120768ce1 [0,-1,0,-65,-927] 1 [13:16:1]&[23:96:1]
120768cf (2 curves)	0	2- 3+ 17+ 37+	2- 3+  2 -4  0  0 17+ -2
Curve Equation t 120768cf1 [0,-1,0,103,345] 2 120768cf2 [0,-1,0,-577,3745] 2
120768cg (4 curves)	0	2- 3+ 17+ 37+	2- 3+ -2  4  4 -2 17+  4
Curve Equation t 120768cg1 [0,-1,0,-244,-806] 2 120768cg2 [0,-1,0,-1689,26649] 4 120768cg3 [0,-1,0,351,84993] 2 120768cg4 [0,-1,0,-26849,1702305] 2
120768ch (1 curve)	0	2- 3+ 17+ 37+	2- 3+  3  3  5  6 17+ -5
Curve Equation t 120768ch1 [0,-1,0,-4929,337761] 1
120768ci (1 curve)	2	2- 3+ 17+ 37+	2- 3+ -3 -1 -3 -4 17+ -3
Curve Equation t Generators 120768ci1 [0,-1,0,-101217,12428289] 1 [75:2292:1]&[173:256:1]
120768cj (1 curve)	0	2- 3+ 17+ 37+	2- 3+ -3  2  0 -1 17+ -3
Curve Equation t 120768cj1 [0,-1,0,-78773537,-401518925631] 1
120768ck (1 curve)	0	2- 3+ 17+ 37+	2- 3+ -3  3  5  4 17+ -5
Curve Equation t 120768ck1 [0,-1,0,-1937,-34479] 1
120768cl (1 curve)	0	2- 3+ 17+ 37+	2- 3+ -3 -3  5  4 17+  7
Curve Equation t 120768cl1 [0,-1,0,-9781857,11779682049] 1
120768cm (1 curve)	1	2- 3+ 17+ 37-	2- 3+  0 -3 -2  1 17+  4
Curve Equation t Generators 120768cm1 [0,-1,0,-439713,-501729471] 1 [2229826824:147907669491:493039]
120768cn (1 curve)	1	2- 3+ 17+ 37-	2- 3+  3  3 -5 -2 17+  7
Curve Equation t Generators 120768cn1 [0,-1,0,111,81] 1 [0:9:1]
120768co (1 curve)	1	2- 3+ 17+ 37-	2- 3+  3 -5  3  2 17+ -5
Curve Equation t Generators 120768co1 [0,-1,0,96,2286] 1 [330:2187:8]
120768cp (1 curve)	1	2- 3+ 17- 37+	2- 3+  1  3 -1  2 17- -3
Curve Equation t Generators 120768cp1 [0,-1,0,-600,-5562] 1 [30690:63153:1000]
120768cq (1 curve)	1	2- 3+ 17- 37+	2- 3+  1  3 -1  6 17- -7
Curve Equation t Generators 120768cq1 [0,-1,0,-4305,-128367] 1 [264:4131:1]
120768cr (1 curve)	2	2- 3+ 17- 37-	2- 3+  0 -3 -6 -1 17- -4
Curve Equation t Generators 120768cr1 [0,-1,0,-713473,-472646495] 1 [1173:17408:1]&[1768:61557:1]
120768cs (1 curve)	0	2- 3+ 17- 37-	2- 3+  1  2  5 -1 17- -1
Curve Equation t 120768cs1 [0,-1,0,-5,1629] 1
120768ct (4 curves)	0	2- 3+ 17- 37-	2- 3+ -2 -4 -4  2 17- -4
Curve Equation t 120768ct1 [0,-1,0,-2513489,-1532944335] 2 120768ct2 [0,-1,0,-2513569,-1532841791] 4 120768ct3 [0,-1,0,-2294529,-1811154015] 2 120768ct4 [0,-1,0,-2733889,-1247968031] 4
120768cu (1 curve)	0	2- 3+ 17- 37-	2- 3+  3  1 -3  4 17- -7
Curve Equation t 120768cu1 [0,-1,0,-1089,-13599] 1
120768cv (1 curve)	0	2- 3+ 17- 37-	2- 3+  3  3  1 -4 17-  3
Curve Equation t 120768cv1 [0,-1,0,260031,-39573279] 1
120768cw (1 curve)	0	2- 3+ 17- 37-	2- 3+  3  3 -3  4 17-  1
Curve Equation t 120768cw1 [0,-1,0,-344,-2754] 1
120768cx (1 curve)	2	2- 3+ 17- 37-	2- 3+ -3  3 -3  2 17- -7
Curve Equation t Generators 120768cx1 [0,-1,0,63,3681] 1 [-9:48:1]&[5:-64:1]
120768cy (1 curve)	1	2- 3- 17+ 37+	2- 3-  0  3  2 -5 17+  8
Curve Equation t Generators 120768cy1 [0,1,0,113087,-26924353] 1 [191:1296:1]
120768cz (1 curve)	1	2- 3- 17+ 37+	2- 3-  1 -1 -3  4 17+  3
Curve Equation t Generators 120768cz1 [0,1,0,120,-558] 1 [21:108:1]
120768da (1 curve)	1	2- 3- 17+ 37+	2- 3-  1 -2  0 -7 17+ -3
Curve Equation t Generators 120768da1 [0,1,0,-4385,110367] 1 [31:72:1]
120768db (1 curve)	1	2- 3- 17+ 37+	2- 3-  1  4 -3 -1 17+  3
Curve Equation t Generators 120768db1 [0,1,0,56407565,-690445068733] 1 [13707272313625693715461470552968975614136414309041759554339978355375853760858701611576991150458504225507913507730946522529776286:2598804525705716479161411801336342644821534387484839515464569933192336782874566767483032719957459121079430674765658956533996756659:392813852626156595613156025594731556093975704693255084014638996381802379028702019278525082448839892920204119182098462013848]
120768dc (1 curve)	1	2- 3- 17+ 37+	2- 3-  1  5 -1  4 17+ -7
Curve Equation t Generators 120768dc1 [0,1,0,2840,25826] 1 [149:1944:1]
120768dd (1 curve)	1	2- 3- 17+ 37+	2- 3- -1 -3 -1  2 17+ -3
Curve Equation t Generators 120768dd1 [0,1,0,-20321,-1121889] 1 [255:3216:1]
120768de (2 curves)	1	2- 3- 17+ 37+	2- 3-  2  0  0  4 17+ -6
Curve Equation t Generators 120768de1 [0,1,0,-40417,6521375] 2 [143:1920:1] 120768de2 [0,1,0,-826497,288724095] 2 [351:6480:1]
120768df (2 curves)	1	2- 3- 17+ 37+	2- 3-  2  4  0  0 17+  2
Curve Equation t Generators 120768df1 [0,1,0,103,-345] 2 [7329:37680:343] 120768df2 [0,1,0,-577,-3745] 2 [91:840:1]
120768dg (4 curves)	1	2- 3- 17+ 37+	2- 3- -2 -4 -4 -2 17+ -4
Curve Equation t Generators 120768dg1 [0,1,0,-244,806] 2 [49:330:1] 120768dg2 [0,1,0,-1689,-26649] 4 [-25:24:1] 120768dg3 [0,1,0,351,-84993] 2 [77:636:1] 120768dg4 [0,1,0,-26849,-1702305] 2 [229:2052:1]
120768dh (2 curves)	1	2- 3- 17+ 37+	2- 3- -3  1  3  4 17+ -1
Curve Equation t Generators 120768dh1 [0,1,0,4863,29439] 1 [63:-768:1] 120768dh2 [0,1,0,-75777,8335359] 1 [159:576:1]
120768di (1 curve)	0	2- 3- 17+ 37-	2- 3- -1 -2 -1  3 17+ -5
Curve Equation t 120768di1 [0,1,0,-721301,-236029389] 1
120768dj (1 curve)	0	2- 3- 17+ 37-	2- 3- -1 -2 -4 -3 17+  7
Curve Equation t 120768dj1 [0,1,0,479,-25249] 1
120768dk (1 curve)	0	2- 3- 17+ 37-	2- 3-  3  5 -3  2 17+  5
Curve Equation t 120768dk1 [0,1,0,96,-2286] 1
120768dl (1 curve)	0	2- 3- 17- 37+	2- 3-  0 -5 -2  5 17-  8
Curve Equation t 120768dl1 [0,1,0,607,48351] 1
120768dm (1 curve)	0	2- 3- 17- 37+	2- 3-  1 -3  1  2 17-  3
Curve Equation t 120768dm1 [0,1,0,-600,5562] 1
120768dn (2 curves)	2	2- 3- 17- 37+	2- 3- -3 -2  3 -5 17- -7
Curve Equation t Generators 120768dn1 [0,1,0,203,-4999] 1 [2180:13209:64]&[128:1461:1] 120768dn2 [0,1,0,-1837,141881] 1 [-32:411:1]&[4152:50653:27]
120768do (1 curve)	1	2- 3- 17- 37-	2- 3-  1  1 -1 -2 17- -5
Curve Equation t Generators 120768do1 [0,1,0,-89505,14083551] 1 [39:3264:1]
120768dp (1 curve)	1	2- 3- 17- 37-	2- 3-  1  2 -1 -5 17-  1
Curve Equation t Generators 120768dp1 [0,1,0,-3000925,2009196377] 1 [2096:70227:1]
120768dq (1 curve)	1	2- 3- 17- 37-	2- 3-  1  5 -1 -2 17-  7
Curve Equation t Generators 120768dq1 [0,1,0,-43745,-3735393] 1 [247:768:1]
120768dr (1 curve)	1	2- 3- 17- 37-	2- 3- -1  1 -1  0 17-  1
Curve Equation t Generators 120768dr1 [0,1,0,-2055521,-1137929697] 1 [12631:1410048:1]
120768ds (1 curve)	1	2- 3- 17- 37-	2- 3- -1 -1 -1  4 17- -5
Curve Equation t Generators 120768ds1 [0,1,0,799,-65889] 1 [55:384:1]
120768dt (1 curve)	1	2- 3- 17- 37-	2- 3- -1 -3 -1 -4 17- -5
Curve Equation t Generators 120768dt1 [0,1,0,1679,-43537] 1 [53:444:1]
120768du (1 curve)	1	2- 3- 17- 37-	2- 3- -1 -5  5  0 17-  1
Curve Equation t Generators 120768du1 [0,1,0,-9314321,10942219983] 1 [1861:-7548:1]
120768dv (4 curves)	1	2- 3- 17- 37-	2- 3- -2 -4 -4 -2 17- -8
Curve Equation t Generators 120768dv1 [0,1,0,1151,-66433] 2 [2884:17985:64] 120768dv2 [0,1,0,-19329,-971649] 4 [209:2040:1] 120768dv3 [0,1,0,-62849,4903551] 4 [-251:2220:1] 120768dv4 [0,1,0,-303489,-64452993] 2 [168205:5541864:125]
120768dw (1 curve)	1	2- 3- 17- 37-	2- 3-  3 -3  3  4 17- -1
Curve Equation t Generators 120768dw1 [0,1,0,-344,2754] 1 [25:102:1]
120768dx (1 curve)	1	2- 3- 17- 37-	2- 3- -3 -2  0 -1 17- -3
Curve Equation t Generators 120768dx1 [0,1,0,63,-2241] 1 [15:48:1]

Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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