Cremona's table of elliptic curves

53312 = 2⁶ · 7² · 17

Class	r	Atkin-Lehner	Eigenvalues
53312a (1 curve)	1	2+ 7+ 17+	2+  1  0 7+  5  5 17+  6
Curve Equation t Generators 53312a1 [0,1,0,2287,-43345] 1 [173603:1215304:6859]
53312b (1 curve)	1	2+ 7+ 17+	2+  1  2 7+  1 -5 17+ -6
Curve Equation t Generators 53312b1 [0,1,0,-14177,-817153] 1 [6753:90944:27]
53312c (1 curve)	1	2+ 7+ 17+	2+ -1  4 7+  3  5 17+ -6
Curve Equation t Generators 53312c1 [0,-1,0,-853841,426823153] 1 [-20571:680120:27]
53312d (1 curve)	1	2+ 7+ 17+	2+  2  1 7+  4 -2 17+  1
Curve Equation t Generators 53312d1 [0,-1,0,-65,1793] 1 [19:84:1]
53312e (2 curves)	1	2+ 7+ 17+	2+  2 -3 7+  0 -2 17+  7
Curve Equation t Generators 53312e1 [0,-1,0,-14177,740321] 1 [-65:1176:1] 53312e2 [0,-1,0,95583,-2881759] 1 [287:6936:1]
53312f (1 curve)	1	2+ 7+ 17+	2+ -2  1 7+ -4 -2 17+ -1
Curve Equation t Generators 53312f1 [0,1,0,-65,-1793] 1 [17:48:1]
53312g (1 curve)	1	2+ 7+ 17+	2+  3 -2 7+ -5  7 17+ -2
Curve Equation t Generators 53312g1 [0,0,0,-17836,2266544] 1 [138:39824:27]
53312h (1 curve)	1	2+ 7+ 17+	2+  3 -4 7+ -1 -3 17+  2
Curve Equation t Generators 53312h1 [0,0,0,-1372,-19600] 1 [956556:3322936:19683]
53312i (1 curve)	1	2+ 7+ 17+	2+ -3  2 7+  5  3 17+  2
Curve Equation t Generators 53312i1 [0,0,0,-97804,42435568] 1 [-471526:7602176:1331]
53312j (1 curve)	0	2+ 7+ 17-	2+  0  1 7+ -2  4 17- -5
Curve Equation t 53312j1 [0,0,0,-20972,-1170512] 1
53312k (1 curve)	0	2+ 7+ 17-	2+  0  1 7+  6 -4 17- -1
Curve Equation t 53312k1 [0,0,0,26068,-22012368] 1
53312l (1 curve)	0	2+ 7- 17+	2+  0 -1 7- -2 -4 17+  5
Curve Equation t 53312l1 [0,0,0,-1027628,401485616] 1
53312m (1 curve)	0	2+ 7- 17+	2+  0 -1 7-  6  4 17+  1
Curve Equation t 53312m1 [0,0,0,532,64176] 1
53312n (4 curves)	0	2+ 7- 17+	2+  0  2 7-  0 -2 17+  4
Curve Equation t 53312n1 [0,0,0,-58604,-5372752] 2 53312n2 [0,0,0,-121324,8149680] 4 53312n3 [0,0,0,411796,60395440] 2 53312n4 [0,0,0,-1657964,821339568] 2
53312o (4 curves)	2	2+ 7- 17+	2+  0 -2 7-  0 -2 17+ -4
Curve Equation t Generators 53312o1 [0,0,0,-2156,-16464] 2 [-40:76:1]&[-10:64:1] 53312o2 [0,0,0,-17836,905520] 4 [-28:1176:1]&[21:735:1] 53312o3 [0,0,0,-2156,2442160] 2 [-42:1568:1]&[4:1560:1] 53312o4 [0,0,0,-284396,58375856] 2 [310:64:1]&[1366:47104:1]
53312p (2 curves)	0	2+ 7- 17+	2+ -2 -2 7-  6  2 17+  0
Curve Equation t 53312p1 [0,1,0,-849,-4145] 2 53312p2 [0,1,0,3071,-28449] 2
53312q (2 curves)	1	2+ 7- 17-	2+  0  0 7-  4  2 17- -4
Curve Equation t Generators 53312q1 [0,0,0,-980,-10976] 2 [36:20:1] 53312q2 [0,0,0,980,-49392] 2 [20853:3011295:1]
53312r (2 curves)	1	2+ 7- 17-	2+  0  0 7- -4  2 17-  4
Curve Equation t Generators 53312r1 [0,0,0,-980,10976] 2 [-35:49:1] 53312r2 [0,0,0,980,49392] 2 [-27:57:1]
53312s (2 curves)	1	2+ 7- 17-	2+  0 -2 7-  2  0 17- -2
Curve Equation t Generators 53312s1 [0,0,0,5684,-82320] 2 [2062:93696:1] 53312s2 [0,0,0,-25676,-696976] 2 [-140:392:1]
53312t (1 curve)	1	2+ 7- 17-	2+  1 -4 7-  3 -5 17-  6
Curve Equation t Generators 53312t1 [0,1,0,-17425,-1249361] 1 [1161:39304:1]
53312u (1 curve)	1	2+ 7- 17-	2+ -1  0 7-  5 -5 17- -6
Curve Equation t Generators 53312u1 [0,-1,0,47,113] 1 [-1:8:1]
53312v (1 curve)	1	2+ 7- 17-	2+ -1 -2 7-  1  5 17-  6
Curve Equation t Generators 53312v1 [0,-1,0,-289,2465] 1 [-7:64:1]
53312w (2 curves)	1	2+ 7- 17-	2+  2  0 7-  2 -2 17-  0
Curve Equation t Generators 53312w1 [0,-1,0,-56513,5166785] 2 [59403:2770048:27] 53312w2 [0,-1,0,-87873,-1174207] 2 [-271:1632:1]
53312x (2 curves)	1	2+ 7- 17-	2+  2  0 7- -2 -6 17-  4
Curve Equation t Generators 53312x1 [0,-1,0,-1633,19041] 2 [915:27636:1] 53312x2 [0,-1,0,-9473,-336895] 2 [-47:48:1]
53312y (1 curve)	1	2+ 7- 17-	2+  2 -1 7- -4  2 17-  1
Curve Equation t Generators 53312y1 [0,-1,0,-3201,608609] 1 [-12271:282024:343]
53312z (2 curves)	1	2+ 7- 17-	2+  2  4 7-  4 -4 17- -6
Curve Equation t Generators 53312z1 [0,-1,0,98719,2283233] 2 [2532372540:274285101223:216000] 53312z2 [0,-1,0,-403041,18841313] 2 [130065:6190856:3375]
53312ba (4 curves)	1	2+ 7- 17-	2+ -2  0 7- -6  2 17- -4
Curve Equation t Generators 53312ba1 [0,1,0,-9473,-222881] 2 [205:2548:1] 53312ba2 [0,1,0,-134913,-19114145] 2 [-213:64:1] 53312ba3 [0,1,0,-323073,70562911] 2 [395:2176:1] 53312ba4 [0,1,0,-354433,56005599] 2 [-85:-9248:1]
53312bb (1 curve)	1	2+ 7- 17-	2+ -2 -1 7-  4  2 17- -1
Curve Equation t Generators 53312bb1 [0,1,0,-3201,-608609] 1 [31305:473684:125]
53312bc (2 curves)	1	2+ 7- 17-	2+ -2  3 7-  0  2 17- -7
Curve Equation t Generators 53312bc1 [0,1,0,-289,-2241] 1 [185:2512:1] 53312bc2 [0,1,0,1951,8959] 1 [25:272:1]
53312bd (2 curves)	1	2+ 7- 17-	2+ -2 -4 7-  6 -2 17-  0
Curve Equation t Generators 53312bd1 [0,1,0,-188225,-3750881] 2 [2893:153860:1] 53312bd2 [0,1,0,-2195265,-1250122721] 2 [-837:1280:1]
53312be (1 curve)	1	2+ 7- 17-	2+  3 -2 7-  5 -3 17- -2
Curve Equation t Generators 53312be1 [0,0,0,-4792396,-14555399824] 1 [588489822852306792275827802053680403710:2600140104492330389579193125335200956416:190328743771170637147413515116260489]
53312bf (1 curve)	1	2+ 7- 17-	2+ -3  2 7- -5 -7 17-  2
Curve Equation t Generators 53312bf1 [0,0,0,-364,-6608] 1 [46:-272:1]
53312bg (1 curve)	1	2+ 7- 17-	2+ -3  4 7- -1  3 17- -2
Curve Equation t Generators 53312bg1 [0,0,0,-67228,6722800] 1 [100:1000:1]
53312bh (1 curve)	0	2- 7+ 17+	2-  1  4 7+ -3  5 17+  6
Curve Equation t 53312bh1 [0,1,0,-853841,-426823153] 1
53312bi (1 curve)	2	2- 7+ 17+	2- -1  0 7+ -5  5 17+ -6
Curve Equation t Generators 53312bi1 [0,-1,0,2287,43345] 1 [33:-392:1]&[23:328:1]
53312bj (1 curve)	0	2- 7+ 17+	2- -1  2 7+ -1 -5 17+  6
Curve Equation t 53312bj1 [0,-1,0,-14177,817153] 1
53312bk (2 curves)	0	2- 7+ 17+	2- -2 -3 7+  0 -2 17+ -7
Curve Equation t 53312bk1 [0,1,0,-14177,-740321] 1 53312bk2 [0,1,0,95583,2881759] 1
53312bl (1 curve)	0	2- 7+ 17+	2-  3  2 7+ -5  3 17+ -2
Curve Equation t 53312bl1 [0,0,0,-97804,-42435568] 1
53312bm (1 curve)	0	2- 7+ 17+	2- -3 -2 7+  5  7 17+  2
Curve Equation t 53312bm1 [0,0,0,-17836,-2266544] 1
53312bn (1 curve)	2	2- 7+ 17+	2- -3 -4 7+  1 -3 17+ -2
Curve Equation t Generators 53312bn1 [0,0,0,-1372,19600] 1 [28:-56:1]&[22:8:1]
53312bo (1 curve)	1	2- 7+ 17-	2-  0  1 7+  2  4 17-  5
Curve Equation t Generators 53312bo1 [0,0,0,-20972,1170512] 1 [112:476:1]
53312bp (1 curve)	1	2- 7+ 17-	2-  0  1 7+ -6 -4 17-  1
Curve Equation t Generators 53312bp1 [0,0,0,26068,22012368] 1 [183280:7084804:125]
53312bq (1 curve)	1	2- 7- 17+	2-  0 -1 7-  2 -4 17+ -5
Curve Equation t Generators 53312bq1 [0,0,0,-1027628,-401485616] 1 [32346456489300528:7340344057370569132:627881709547]
53312br (1 curve)	1	2- 7- 17+	2-  0 -1 7- -6  4 17+ -1
Curve Equation t Generators 53312br1 [0,0,0,532,-64176] 1 [464:10004:1]
53312bs (4 curves)	1	2- 7- 17+	2-  0  2 7-  0 -2 17+ -4
Curve Equation t Generators 53312bs1 [0,0,0,-58604,5372752] 2 [4956:348488:1] 53312bs2 [0,0,0,-121324,-8149680] 4 [16733446310:191796643584:37595375] 53312bs3 [0,0,0,411796,-60395440] 2 [73234303325820:5187933030864520:14832537993] 53312bs4 [0,0,0,-1657964,-821339568] 2 [219730:5147744:125]
53312bt (4 curves)	1	2- 7- 17+	2-  0 -2 7-  0 -2 17+  4
Curve Equation t Generators 53312bt1 [0,0,0,-2156,16464] 2 [74:512:1] 53312bt2 [0,0,0,-17836,-905520] 4 [172:1056:1] 53312bt3 [0,0,0,-2156,-2442160] 2 [211684:1480800:1331] 53312bt4 [0,0,0,-284396,-58375856] 2 [84612:-4662944:27]
53312bu (2 curves)	1	2- 7- 17+	2-  2  2 7-  2  2 17+ -4
Curve Equation t Generators 53312bu1 [0,-1,0,-212,-2470] 2 [14059777605:1222026037910:1860867] 53312bu2 [0,-1,0,-4377,-109927] 2 [30221:5253576:1]
53312bv (2 curves)	1	2- 7- 17+	2-  2 -2 7- -6  2 17+  0
Curve Equation t Generators 53312bv1 [0,-1,0,-849,4145] 2 [77:624:1] 53312bv2 [0,-1,0,3071,28449] 2 [1785:19396:27]
53312bw (2 curves)	1	2- 7- 17+	2- -2  2 7- -2  2 17+  4
Curve Equation t Generators 53312bw1 [0,1,0,-212,2470] 2 [-15:50:1] 53312bw2 [0,1,0,-4377,109927] 2 [-61:392:1]
53312bx (2 curves)	0	2- 7- 17-	2-  0 -2 7- -2  0 17-  2
Curve Equation t 53312bx1 [0,0,0,5684,82320] 2 53312bx2 [0,0,0,-25676,696976] 2
53312by (1 curve)	2	2- 7- 17-	2-  1  0 7- -5 -5 17-  6
Curve Equation t Generators 53312by1 [0,1,0,47,-113] 1 [3:8:1]&[69:580:1]
53312bz (1 curve)	0	2- 7- 17-	2-  1 -2 7- -1  5 17- -6
Curve Equation t 53312bz1 [0,1,0,-289,-2465] 1
53312ca (1 curve)	2	2- 7- 17-	2- -1 -4 7- -3 -5 17- -6
Curve Equation t Generators 53312ca1 [0,-1,0,-17425,1249361] 1 [-5:1156:1]&[41:776:1]
53312cb (4 curves)	0	2- 7- 17-	2-  2  0 7-  6  2 17-  4
Curve Equation t 53312cb1 [0,-1,0,-9473,222881] 2 53312cb2 [0,-1,0,-134913,19114145] 2 53312cb3 [0,-1,0,-323073,-70562911] 2 53312cb4 [0,-1,0,-354433,-56005599] 2
53312cc (2 curves)	0	2- 7- 17-	2-  2  0 7- -6  6 17- -4
Curve Equation t 53312cc1 [0,-1,0,-54553,-4886055] 2 53312cc2 [0,-1,0,-56513,-4514047] 2
53312cd (2 curves)	0	2- 7- 17-	2-  2  3 7-  0  2 17-  7
Curve Equation t 53312cd1 [0,-1,0,-289,2241] 1 53312cd2 [0,-1,0,1951,-8959] 1
53312ce (2 curves)	0	2- 7- 17-	2-  2  4 7- -2  2 17-  8
Curve Equation t 53312ce1 [0,-1,0,-1241,-15847] 2 53312ce2 [0,-1,0,-3201,48833] 2
53312cf (2 curves)	2	2- 7- 17-	2-  2 -4 7- -6 -2 17-  0
Curve Equation t Generators 53312cf1 [0,-1,0,-188225,3750881] 2 [7:1560:1]&[439:2352:1] 53312cf2 [0,-1,0,-2195265,1250122721] 2 [-1381:40572:1]&[581:13056:1]
53312cg (2 curves)	2	2- 7- 17-	2- -2  0 7-  2 -6 17- -4
Curve Equation t Generators 53312cg1 [0,1,0,-1633,-19041] 2 [-17:64:1]&[-15:48:1] 53312cg2 [0,1,0,-9473,336895] 2 [31:272:1]&[-54:833:1]
53312ch (2 curves)	2	2- 7- 17-	2- -2  0 7- -2 -2 17-  0
Curve Equation t Generators 53312ch1 [0,1,0,-56513,-5166785] 2 [-143:104:1]&[367:4864:1] 53312ch2 [0,1,0,-87873,1174207] 2 [-187:3332:1]&[-17:1632:1]
53312ci (2 curves)	0	2- 7- 17-	2- -2  0 7-  6  6 17-  4
Curve Equation t 53312ci1 [0,1,0,-54553,4886055] 2 53312ci2 [0,1,0,-56513,4514047] 2
53312cj (2 curves)	0	2- 7- 17-	2- -2  4 7-  2  2 17- -8
Curve Equation t 53312cj1 [0,1,0,-1241,15847] 2 53312cj2 [0,1,0,-3201,-48833] 2
53312ck (2 curves)	0	2- 7- 17-	2- -2  4 7- -4 -4 17-  6
Curve Equation t 53312ck1 [0,1,0,98719,-2283233] 2 53312ck2 [0,1,0,-403041,-18841313] 2
53312cl (1 curve)	0	2- 7- 17-	2-  3  2 7-  5 -7 17- -2
Curve Equation t 53312cl1 [0,0,0,-364,6608] 1
53312cm (1 curve)	0	2- 7- 17-	2-  3  4 7-  1  3 17-  2
Curve Equation t 53312cm1 [0,0,0,-67228,-6722800] 1
53312cn (1 curve)	0	2- 7- 17-	2- -3 -2 7- -5 -3 17-  2
Curve Equation t 53312cn1 [0,0,0,-4792396,14555399824] 1

Data from Elliptic Curve Data by J. E. Cremona.
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