Cremona's table of elliptic curves

81984 = 2⁶ · 3 · 7 · 61

Class	r	Atkin-Lehner	Eigenvalues
81984a (1 curve)	1	2+ 3+ 7+ 61+	2+ 3+  0 7+ -2 -4 -3  6
Curve Equation t Generators 81984a1 [0,-1,0,-103,445] 1 [4:9:1]
81984b (1 curve)	1	2+ 3+ 7+ 61+	2+ 3+  0 7+ -3 -1  6  2
Curve Equation t Generators 81984b1 [0,-1,0,-33,-927] 1 [17:56:1]
81984c (1 curve)	1	2+ 3+ 7+ 61+	2+ 3+  4 7+  0 -4 -3  4
Curve Equation t Generators 81984c1 [0,-1,0,-1701,-1140867] 1 [513888540:9219440319:1520875]
81984d (1 curve)	1	2+ 3+ 7+ 61+	2+ 3+ -4 7+  4 -4  5  0
Curve Equation t Generators 81984d1 [0,-1,0,-13685,620781] 1 [68:3:1]
81984e (1 curve)	0	2+ 3+ 7+ 61-	2+ 3+  0 7+  1  1  2 -6
Curve Equation t 81984e1 [0,-1,0,1567,157281] 1
81984f (1 curve)	0	2+ 3+ 7+ 61-	2+ 3+  0 7+ -4 -4  7  4
Curve Equation t 81984f1 [0,-1,0,-6473,555363] 1
81984g (1 curve)	2	2+ 3+ 7+ 61-	2+ 3+  1 7+ -2  0  0 -1
Curve Equation t Generators 81984g1 [0,-1,0,-385,3073] 1 [3:44:1]&[9:-16:1]
81984h (4 curves)	0	2+ 3+ 7+ 61-	2+ 3+ -2 7+ -4  6  6  4
Curve Equation t 81984h1 [0,-1,0,-5124,-139482] 2 81984h2 [0,-1,0,-5129,-139191] 4 81984h3 [0,-1,0,-2689,-274367] 2 81984h4 [0,-1,0,-7649,14529] 4
81984i (1 curve)	0	2+ 3+ 7+ 61-	2+ 3+  3 7+ -2  4 -4  3
Curve Equation t 81984i1 [0,-1,0,-15489,771201] 1
81984j (1 curve)	0	2+ 3+ 7+ 61-	2+ 3+ -3 7+ -4  2  4  1
Curve Equation t 81984j1 [0,-1,0,-1042497,-1904374719] 1
81984k (4 curves)	0	2+ 3+ 7- 61+	2+ 3+  0 7-  0 -2 -6  4
Curve Equation t 81984k1 [0,-1,0,-1653,-4518891] 2 81984k2 [0,-1,0,-420113,-103191759] 2 81984k3 [0,-1,0,-2118453,-1186158987] 2 81984k4 [0,-1,0,-33895793,-75945529071] 2
81984l (3 curves)	0	2+ 3+ 7- 61+	2+ 3+  0 7- -3 -5  6 -2
Curve Equation t 81984l1 [0,-1,0,-5153,176289] 1 81984l2 [0,-1,0,38047,-1442847] 1 81984l3 [0,-1,0,-723233,-241292895] 1
81984m (1 curve)	0	2+ 3+ 7- 61+	2+ 3+  1 7-  0 -2  8 -7
Curve Equation t 81984m1 [0,-1,0,-2842145,-1843294047] 1
81984n (4 curves)	0	2+ 3+ 7- 61+	2+ 3+  2 7-  0  2  6  4
Curve Equation t 81984n1 [0,-1,0,-3997,98605] 2 81984n2 [0,-1,0,-4177,89425] 4 81984n3 [0,-1,0,7583,491617] 2 81984n4 [0,-1,0,-18817,-903167] 2
81984o (2 curves)	0	2+ 3+ 7- 61+	2+ 3+  3 7- -6  4  0  7
Curve Equation t 81984o1 [0,-1,0,-11809,-586079] 1 81984o2 [0,-1,0,-1007329,-388803743] 1
81984p (2 curves)	2	2+ 3+ 7- 61+	2+ 3+ -3 7-  0 -2  0  1
Curve Equation t Generators 81984p1 [0,-1,0,384223,-43961439] 1 [115:1316:1]&[3097:175616:1] 81984p2 [0,-1,0,-7189217,-7575582879] 1 [3721:131072:1]&[4399:214256:1]
81984q (2 curves)	0	2+ 3+ 7- 61+	2+ 3+ -3 7-  0  4  3 -2
Curve Equation t 81984q1 [0,-1,0,-83937,10560609] 1 81984q2 [0,-1,0,560223,-36931551] 1
81984r (4 curves)	1	2+ 3+ 7- 61-	2+ 3+  2 7- -4 -2 -2  4
Curve Equation t Generators 81984r1 [0,-1,0,-812,7038] 2 [164610:2075241:1000] 81984r2 [0,-1,0,-4457,-107415] 4 [655:16660:1] 81984r3 [0,-1,0,3103,-441567] 2 [223909:5732740:343] 81984r4 [0,-1,0,-70337,-7156575] 2 [3330011:78622460:4913]
81984s (2 curves)	0	2+ 3- 7+ 61+	2+ 3-  0 7+ -4  6  6  4
Curve Equation t 81984s1 [0,1,0,-533,-6021] 2 81984s2 [0,1,0,-9073,-335665] 2
81984t (1 curve)	2	2+ 3- 7+ 61+	2+ 3- -1 7+ -2 -4  0 -7
Curve Equation t Generators 81984t1 [0,1,0,81759,86463] 1 [3:576:1]&[579:15552:1]
81984u (1 curve)	0	2+ 3- 7+ 61+	2+ 3-  3 7+ -4  0 -3 -2
Curve Equation t 81984u1 [0,1,0,-358209,-125989857] 1
81984v (1 curve)	2	2+ 3- 7+ 61+	2+ 3- -3 7+ -4  2  0 -5
Curve Equation t Generators 81984v1 [0,1,0,223,-2241] 1 [9:24:1]&[19:-96:1]
81984w (1 curve)	0	2+ 3- 7+ 61+	2+ 3- -4 7+  5  7 -2 -2
Curve Equation t 81984w1 [0,1,0,-225,4479] 1
81984x (1 curve)	1	2+ 3- 7+ 61-	2+ 3-  0 7+  4  4  3  4
Curve Equation t Generators 81984x1 [0,1,0,-1793,33417] 1 [-32:243:1]
81984y (1 curve)	1	2+ 3- 7+ 61-	2+ 3- -1 7+  0  4  3 -6
Curve Equation t Generators 81984y1 [0,1,0,-161,6591] 1 [-3:84:1]
81984z (4 curves)	1	2+ 3- 7+ 61-	2+ 3-  2 7+  4 -2 -2 -4
Curve Equation t Generators 81984z1 [0,1,0,-812,-7038] 2 [266:495:8] 81984z2 [0,1,0,-4457,107415] 4 [-5:360:1] 81984z3 [0,1,0,3103,441567] 2 [37:780:1] 81984z4 [0,1,0,-70337,7156575] 2 [178:555:1]
81984ba (1 curve)	1	2+ 3- 7+ 61-	2+ 3- -4 7+  3  1  6  6
Curve Equation t Generators 81984ba1 [0,1,0,-2529665,1547772639] 1 [907:-576:1]
81984bb (1 curve)	1	2+ 3- 7- 61+	2+ 3-  0 7-  2 -4 -3 -6
Curve Equation t Generators 81984bb1 [0,1,0,-103,-445] 1 [26:123:1]
81984bc (1 curve)	1	2+ 3- 7- 61+	2+ 3-  0 7-  3 -1  6 -2
Curve Equation t Generators 81984bc1 [0,1,0,-33,927] 1 [-9:24:1]
81984bd (1 curve)	1	2+ 3- 7- 61+	2+ 3-  3 7- -4  0 -7 -2
Curve Equation t Generators 81984bd1 [0,1,0,16191,123039] 1 [315:6048:1]
81984be (1 curve)	0	2+ 3- 7- 61-	2+ 3-  0 7-  0 -4  3  0
Curve Equation t 81984be1 [0,1,0,27,387] 1
81984bf (1 curve)	0	2+ 3- 7- 61-	2+ 3-  1 7-  4  2  4 -1
Curve Equation t 81984bf1 [0,1,0,-705,-25953] 1
81984bg (1 curve)	0	2+ 3- 7- 61-	2+ 3- -1 7-  2  4 -4  5
Curve Equation t 81984bg1 [0,1,0,9919,1303071] 1
81984bh (4 curves)	0	2+ 3- 7- 61-	2+ 3-  2 7- -4 -2  2 -4
Curve Equation t 81984bh1 [0,1,0,-16737,810495] 2 81984bh2 [0,1,0,-37217,-1585665] 4 81984bh3 [0,1,0,118943,-11298817] 4 81984bh4 [0,1,0,-521057,-144899073] 2
81984bi (4 curves)	0	2+ 3- 7- 61-	2+ 3- -2 7-  4  6  6 -4
Curve Equation t 81984bi1 [0,1,0,-5124,139482] 2 81984bi2 [0,1,0,-5129,139191] 4 81984bi3 [0,1,0,-2689,274367] 4 81984bi4 [0,1,0,-7649,-14529] 2
81984bj (1 curve)	0	2+ 3- 7- 61-	2+ 3-  3 7-  0  4 -5 -6
Curve Equation t 81984bj1 [0,1,0,-7649,-260481] 1
81984bk (1 curve)	2	2+ 3- 7- 61-	2+ 3- -3 7- -2 -4 -8  5
Curve Equation t Generators 81984bk1 [0,1,0,-4417,223391] 1 [-77:336:1]&[35:-336:1]
81984bl (1 curve)	0	2- 3+ 7+ 61+	2- 3+  3 7+  4  0 -7  2
Curve Equation t 81984bl1 [0,-1,0,16191,-123039] 1
81984bm (1 curve)	1	2- 3+ 7+ 61-	2- 3+  0 7+  0 -4  3  0
Curve Equation t Generators 81984bm1 [0,-1,0,27,-387] 1 [12:39:1]
81984bn (1 curve)	1	2- 3+ 7+ 61-	2- 3+  1 7+ -4  2  4  1
Curve Equation t Generators 81984bn1 [0,-1,0,-705,25953] 1 [-37:4:1]
81984bo (1 curve)	1	2- 3+ 7+ 61-	2- 3+ -1 7+  0  2  4 -7
Curve Equation t Generators 81984bo1 [0,-1,0,-41356,3250954] 1 [75:752:1]
81984bp (1 curve)	1	2- 3+ 7+ 61-	2- 3+ -1 7+ -2  4 -4 -5
Curve Equation t Generators 81984bp1 [0,-1,0,9919,-1303071] 1 [11855:86756:125]
81984bq (4 curves)	1	2- 3+ 7+ 61-	2- 3+  2 7+  4 -2  2  4
Curve Equation t Generators 81984bq1 [0,-1,0,-16737,-810495] 2 [245372848535:-33737763119104:12977875] 81984bq2 [0,-1,0,-37217,1585665] 4 [59345:151340:1331] 81984bq3 [0,-1,0,118943,11298817] 2 [-110042237024:654794612505:1263214441] 81984bq4 [0,-1,0,-521057,144899073] 4 [115020302560:-31629506504453:1520875]
81984br (1 curve)	1	2- 3+ 7+ 61-	2- 3+  3 7+  0  4 -5  6
Curve Equation t Generators 81984br1 [0,-1,0,-7649,260481] 1 [55:56:1]
81984bs (1 curve)	1	2- 3+ 7+ 61-	2- 3+  3 7+  4 -2  4 -3
Curve Equation t Generators 81984bs1 [0,-1,0,1867476,-2224803654] 1 [15125388520355020906415:2563838058398163942416884:527555243500993261]
81984bt (1 curve)	1	2- 3+ 7+ 61-	2- 3+ -3 7+  2 -4 -8 -5
Curve Equation t Generators 81984bt1 [0,-1,0,-4417,-223391] 1 [87:208:1]
81984bu (2 curves)	1	2- 3+ 7+ 61-	2- 3+ -4 7+  0  2 -2 -4
Curve Equation t Generators 81984bu1 [0,-1,0,-560,-4914] 2 [234:429:8] 81984bu2 [0,-1,0,-425,-7479] 2 [55:364:1]
81984bv (2 curves)	1	2- 3+ 7- 61+	2- 3+  0 7-  4  6  6 -4
Curve Equation t Generators 81984bv1 [0,-1,0,-533,6021] 2 [-20:91:1] 81984bv2 [0,-1,0,-9073,335665] 2 [224:3081:1]
81984bw (1 curve)	1	2- 3+ 7- 61+	2- 3+ -1 7-  0 -6  0  5
Curve Equation t Generators 81984bw1 [0,-1,0,-36,162] 1 [-1:14:1]
81984bx (1 curve)	1	2- 3+ 7- 61+	2- 3+ -1 7-  2 -4  0  7
Curve Equation t Generators 81984bx1 [0,-1,0,81759,-86463] 1 [71:2464:1]
81984by (1 curve)	1	2- 3+ 7- 61+	2- 3+  3 7-  4  0 -3  2
Curve Equation t Generators 81984by1 [0,-1,0,-358209,125989857] 1 [2629:131712:1]
81984bz (1 curve)	1	2- 3+ 7- 61+	2- 3+ -3 7-  4  2  0  5
Curve Equation t Generators 81984bz1 [0,-1,0,223,2241] 1 [7:64:1]
81984ca (1 curve)	1	2- 3+ 7- 61+	2- 3+ -4 7- -5  7 -2  2
Curve Equation t Generators 81984ca1 [0,-1,0,-225,-4479] 1 [29:112:1]
81984cb (1 curve)	0	2- 3+ 7- 61-	2- 3+  0 7- -4  4  3 -4
Curve Equation t 81984cb1 [0,-1,0,-1793,-33417] 1
81984cc (1 curve)	0	2- 3+ 7- 61-	2- 3+ -1 7-  0  4  3  6
Curve Equation t 81984cc1 [0,-1,0,-161,-6591] 1
81984cd (1 curve)	0	2- 3+ 7- 61-	2- 3+  4 7- -2  4  7 -2
Curve Equation t 81984cd1 [0,-1,0,429,-3087] 1
81984ce (1 curve)	0	2- 3+ 7- 61-	2- 3+ -4 7- -3  1  6 -6
Curve Equation t 81984ce1 [0,-1,0,-2529665,-1547772639] 1
81984cf (4 curves)	1	2- 3- 7+ 61+	2- 3-  0 7+  0 -2 -6 -4
Curve Equation t Generators 81984cf1 [0,1,0,-1653,4518891] 2 [75:2196:1] 81984cf2 [0,1,0,-420113,103191759] 2 [-635:10692:1] 81984cf3 [0,1,0,-2118453,1186158987] 2 [846:399:1] 81984cf4 [0,1,0,-33895793,75945529071] 2 [-971:328548:1]
81984cg (3 curves)	1	2- 3- 7+ 61+	2- 3-  0 7+  3 -5  6  2
Curve Equation t Generators 81984cg1 [0,1,0,-5153,-176289] 1 [199:-2592:1] 81984cg2 [0,1,0,38047,1442847] 1 [151:3264:1] 81984cg3 [0,1,0,-723233,241292895] 1 [641157:2950656:1331]
81984ch (1 curve)	1	2- 3- 7+ 61+	2- 3-  1 7+  0 -2  8  7
Curve Equation t Generators 81984ch1 [0,1,0,-2842145,1843294047] 1 [961:648:1]
81984ci (1 curve)	1	2- 3- 7+ 61+	2- 3- -1 7+  0 -6  0 -5
Curve Equation t Generators 81984ci1 [0,1,0,-36,-162] 1 [9:18:1]
81984cj (4 curves)	1	2- 3- 7+ 61+	2- 3-  2 7+  0  2  6 -4
Curve Equation t Generators 81984cj1 [0,1,0,-3997,-98605] 2 [326:5775:1] 81984cj2 [0,1,0,-4177,-89425] 4 [434038:7684425:1331] 81984cj3 [0,1,0,7583,-491617] 2 [2088622822:-38473917225:6539203] 81984cj4 [0,1,0,-18817,903167] 2 [10558300925:-74262614316:76765625]
81984ck (2 curves)	1	2- 3- 7+ 61+	2- 3-  3 7+  6  4  0 -7
Curve Equation t Generators 81984ck1 [0,1,0,-11809,586079] 1 [65:312:1] 81984ck2 [0,1,0,-1007329,388803743] 1 [46044787:140712:79507]
81984cl (2 curves)	1	2- 3- 7+ 61+	2- 3- -3 7+  0 -2  0 -1
Curve Equation t Generators 81984cl1 [0,1,0,384223,43961439] 1 [625:22992:1] 81984cl2 [0,1,0,-7189217,7575582879] 1 [6959379051:57302202864:4330747]
81984cm (2 curves)	1	2- 3- 7+ 61+	2- 3- -3 7+  0  4  3  2
Curve Equation t Generators 81984cm1 [0,1,0,-83937,-10560609] 1 [417:5208:1] 81984cm2 [0,1,0,560223,36931551] 1 [50982667:5351631432:571787]
81984cn (1 curve)	0	2- 3- 7+ 61-	2- 3-  4 7+  2  4  7  2
Curve Equation t 81984cn1 [0,1,0,429,3087] 1
81984co (1 curve)	0	2- 3- 7- 61+	2- 3-  4 7-  0 -4 -3 -4
Curve Equation t 81984co1 [0,1,0,-1701,1140867] 1
81984cp (1 curve)	0	2- 3- 7- 61+	2- 3- -4 7- -4 -4  5  0
Curve Equation t 81984cp1 [0,1,0,-13685,-620781] 1
81984cq (1 curve)	1	2- 3- 7- 61-	2- 3-  0 7- -1  1  2  6
Curve Equation t Generators 81984cq1 [0,1,0,1567,-157281] 1 [471345:17485824:343]
81984cr (1 curve)	1	2- 3- 7- 61-	2- 3-  0 7-  4 -4  7 -4
Curve Equation t Generators 81984cr1 [0,1,0,-6473,-555363] 1 [148:1323:1]
81984cs (1 curve)	1	2- 3- 7- 61-	2- 3-  1 7-  2  0  0  1
Curve Equation t Generators 81984cs1 [0,1,0,-385,-3073] 1 [264401:1804944:4913]
81984ct (1 curve)	1	2- 3- 7- 61-	2- 3- -1 7-  0  2  4  7
Curve Equation t Generators 81984ct1 [0,1,0,-41356,-3250954] 1 [245:1176:1]
81984cu (1 curve)	1	2- 3- 7- 61-	2- 3-  3 7-  2  4 -4 -3
Curve Equation t Generators 81984cu1 [0,1,0,-15489,-771201] 1 [165:1092:1]
81984cv (1 curve)	1	2- 3- 7- 61-	2- 3-  3 7- -4 -2  4  3
Curve Equation t Generators 81984cv1 [0,1,0,1867476,2224803654] 1 [2325:138348:1]
81984cw (1 curve)	1	2- 3- 7- 61-	2- 3- -3 7-  4  2  4 -1
Curve Equation t Generators 81984cw1 [0,1,0,-1042497,1904374719] 1 [-891:46116:1]
81984cx (2 curves)	1	2- 3- 7- 61-	2- 3- -4 7-  0  2 -2  4
Curve Equation t Generators 81984cx1 [0,1,0,-560,4914] 2 [1:66:1] 81984cx2 [0,1,0,-425,7479] 2 [1:84:1]

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