Cremona's table of elliptic curves

81312 = 2⁵ · 3 · 7 · 11²

Class	r	Atkin-Lehner	Eigenvalues
81312a (2 curves)	1	2+ 3+ 7+ 11+	2+ 3+  0 7+ 11+  2  6 -6
Curve Equation t Generators 81312a1 [0,-1,0,-587858,173677704] 2 [-204:16884:1] 81312a2 [0,-1,0,-601168,165414856] 2 [-1213686:-97843249:5832]
81312b (1 curve)	0	2+ 3+ 7+ 11-	2+ 3+  1 7+ 11-  4 -5  2
Curve Equation t 81312b1 [0,-1,0,-1085,-12747] 1
81312c (4 curves)	0	2+ 3+ 7+ 11-	2+ 3+  2 7+ 11-  2 -6  0
Curve Equation t 81312c1 [0,-1,0,-72882,-1305720] 4 81312c2 [0,-1,0,286488,-10649340] 2 81312c3 [0,-1,0,-725072,236613192] 2 81312c4 [0,-1,0,-873297,-313307487] 2
81312d (4 curves)	0	2+ 3+ 7+ 11-	2+ 3+ -2 7+ 11- -2 -2 -4
Curve Equation t 81312d1 [0,-1,0,-391354,94330744] 4 81312d2 [0,-1,0,-332064,123833448] 2 81312d3 [0,-1,0,-451249,63604609] 2 81312d4 [0,-1,0,-6261064,6032129380] 4
81312e (4 curves)	0	2+ 3+ 7+ 11-	2+ 3+ -2 7+ 11-  6  2  4
Curve Equation t 81312e1 [0,-1,0,-1734,-25056] 4 81312e2 [0,-1,0,1896,-119436] 2 81312e3 [0,-1,0,-5969,150273] 2 81312e4 [0,-1,0,-27144,-1712280] 2
81312f (1 curve)	0	2+ 3+ 7+ 11-	2+ 3+  3 7+ 11-  0 -5  2
Curve Equation t 81312f1 [0,-1,0,-748909,-249198299] 1
81312g (1 curve)	0	2+ 3+ 7+ 11-	2+ 3+  3 7+ 11-  4  7  6
Curve Equation t 81312g1 [0,-1,0,-3549,-71883] 1
81312h (1 curve)	2	2+ 3+ 7+ 11-	2+ 3+ -3 7+ 11-  3  3 -6
Curve Equation t Generators 81312h1 [0,-1,0,-40817,9106209] 1 [-256:1647:1]&[-161:3388:1]
81312i (2 curves)	0	2+ 3+ 7+ 11-	2+ 3+  4 7+ 11- -6  0  2
Curve Equation t 81312i1 [0,-1,0,1654,35928] 2 81312i2 [0,-1,0,-11656,381988] 2
81312j (1 curve)	1	2+ 3+ 7- 11-	2+ 3+ -1 7- 11-  4  5  2
Curve Equation t Generators 81312j1 [0,-1,0,-19741,-1061003] 1 [-81:4:1]
81312k (4 curves)	1	2+ 3+ 7- 11-	2+ 3+  2 7- 11- -2  2  8
Curve Equation t Generators 81312k1 [0,-1,0,-9962,146280] 4 [6280:82215:512] 81312k2 [0,-1,0,36623,1087297] 2 [-313489449:11736787040:17779581] 81312k3 [0,-1,0,-86192,-9611160] 2 [-66790584:-83793905:373248] 81312k4 [0,-1,0,-129752,18018948] 4 [101:2436:1]
81312l (4 curves)	1	2+ 3+ 7- 11-	2+ 3+  2 7- 11- -2 -2 -4
Curve Equation t Generators 81312l1 [0,-1,0,-2702,-42480] 4 [3832:237160:1] 81312l2 [0,-1,0,5768,-262700] 2 [868924:3544155:21952] 81312l3 [0,-1,0,-13592,576072] 2 [53:42:1] 81312l4 [0,-1,0,-40817,-3160287] 2 [-935020:58793:8000]
81312m (1 curve)	1	2+ 3+ 7- 11-	2+ 3+ -2 7- 11-  1  6  0
Curve Equation t Generators 81312m1 [0,-1,0,-7784,-276252] 1 [136:1078:1]
81312n (4 curves)	1	2+ 3+ 7- 11-	2+ 3+ -2 7- 11-  2 -2  4
Curve Equation t Generators 81312n1 [0,-1,0,-18674,-968856] 4 [5735:434148:1] 81312n2 [0,-1,0,-5969,-2277471] 2 [367012:27787565:64] 81312n3 [0,-1,0,-31984,607048] 2 [-83:1638:1] 81312n4 [0,-1,0,-298184,-62572860] 2 [-245271172:1111877:778688]
81312o (2 curves)	1	2+ 3+ 7- 11-	2+ 3+ -4 7- 11-  2  0 -4
Curve Equation t Generators 81312o1 [0,-1,0,25370,2246356] 2 [-24:1274:1] 81312o2 [0,-1,0,-182145,23620401] 2 [-339:6804:1]
81312p (2 curves)	2	2+ 3- 7+ 11+	2+ 3-  0 7+ 11+ -2 -6 -6
Curve Equation t Generators 81312p1 [0,1,0,-4858,128720] 2 [41:-12:1]&[-10:420:1] 81312p2 [0,1,0,-4968,122472] 2 [66:294:1]&[-6:390:1]
81312q (2 curves)	1	2+ 3- 7+ 11-	2+ 3-  0 7+ 11-  2 -4 -4
Curve Equation t Generators 81312q1 [0,1,0,202,6180] 2 [66:558:1] 81312q2 [0,1,0,-4033,91727] 2 [23:108:1]
81312r (2 curves)	1	2+ 3- 7+ 11-	2+ 3-  0 7+ 11-  2 -4  6
Curve Equation t Generators 81312r1 [0,1,0,-2906218,-41302279504] 2 [2646413665:18690901476:704969] 81312r2 [0,1,0,-197777928,-1060715168856] 2 [16290:201318:1]
81312s (1 curve)	1	2+ 3- 7+ 11-	2+ 3-  1 7+ 11- -4  5  2
Curve Equation t Generators 81312s1 [0,1,0,-131325,-17491509] 1 [-231:756:1]
81312t (4 curves)	1	2+ 3- 7+ 11-	2+ 3-  2 7+ 11- -2 -2  4
Curve Equation t Generators 81312t1 [0,1,0,-2702,42480] 4 [16:60:1] 81312t2 [0,1,0,5768,262700] 2 [863:25470:1] 81312t3 [0,1,0,-13592,-576072] 2 [-598:1335:8] 81312t4 [0,1,0,-40817,3160287] 2 [6986:201465:8]
81312u (1 curve)	1	2+ 3- 7+ 11-	2+ 3-  3 7+ 11- -4 -7  6
Curve Equation t Generators 81312u1 [0,1,0,-429469,-97394101] 1 [-106645:852396:343]
81312v (1 curve)	0	2+ 3- 7- 11-	2+ 3- -1 7- 11- -4 -5  2
Curve Equation t 81312v1 [0,1,0,-2388701,-1421749749] 1
81312w (1 curve)	0	2+ 3- 7- 11-	2+ 3- -2 7- 11- -1 -6  0
Curve Equation t 81312w1 [0,1,0,-941904,-371458980] 1
81312x (4 curves)	0	2+ 3- 7- 11-	2+ 3- -2 7- 11-  6  2 -4
Curve Equation t 81312x1 [0,1,0,-1734,25056] 4 81312x2 [0,1,0,1896,119436] 2 81312x3 [0,1,0,-5969,-150273] 2 81312x4 [0,1,0,-27144,1712280] 2
81312y (1 curve)	0	2+ 3- 7- 11-	2+ 3-  3 7- 11-  0 -5 -2
Curve Equation t 81312y1 [0,1,0,-748909,249198299] 1
81312z (1 curve)	0	2+ 3- 7- 11-	2+ 3- -3 7- 11-  3  3  6
Curve Equation t 81312z1 [0,1,0,-40817,-9106209] 1
81312ba (1 curve)	1	2- 3+ 7+ 11-	2- 3+ -1 7+ 11- -4 -5 -2
Curve Equation t Generators 81312ba1 [0,-1,0,-2388701,1421749749] 1 [807:4356:1]
81312bb (1 curve)	1	2- 3+ 7+ 11-	2- 3+ -2 7+ 11- -1 -6  0
Curve Equation t Generators 81312bb1 [0,-1,0,-941904,371458980] 1 [392:7894:1]
81312bc (2 curves)	1	2- 3+ 7- 11+	2- 3+  0 7- 11+ -2 -6  6
Curve Equation t Generators 81312bc1 [0,-1,0,-4858,-128720] 2 [1368:50512:1] 81312bc2 [0,-1,0,-4968,-122472] 2 [-31:28:1]
81312bd (2 curves)	0	2- 3+ 7- 11-	2- 3+  0 7- 11-  2 -4  4
Curve Equation t 81312bd1 [0,-1,0,202,-6180] 2 81312bd2 [0,-1,0,-4033,-91727] 2
81312be (2 curves)	0	2- 3+ 7- 11-	2- 3+  0 7- 11-  2 -4 -6
Curve Equation t 81312be1 [0,-1,0,-2906218,41302279504] 2 81312be2 [0,-1,0,-197777928,1060715168856] 2
81312bf (1 curve)	0	2- 3+ 7- 11-	2- 3+  1 7- 11- -4  5 -2
Curve Equation t 81312bf1 [0,-1,0,-131325,17491509] 1
81312bg (4 curves)	0	2- 3+ 7- 11-	2- 3+ -2 7- 11-  2  2 -4
Curve Equation t 81312bg1 [0,-1,0,-6574,-165416] 4 81312bg2 [0,-1,0,13391,-991967] 4 81312bg3 [0,-1,0,-31984,2060500] 2 81312bg4 [0,-1,0,-99744,-12091176] 2
81312bh (1 curve)	0	2- 3+ 7- 11-	2- 3+  3 7- 11-  0  5 -2
Curve Equation t 81312bh1 [0,-1,0,-6189,189477] 1
81312bi (1 curve)	0	2- 3+ 7- 11-	2- 3+  3 7- 11- -4 -7 -6
Curve Equation t 81312bi1 [0,-1,0,-429469,97394101] 1
81312bj (1 curve)	2	2- 3+ 7- 11-	2- 3+ -3 7- 11- -3 -3  6
Curve Equation t Generators 81312bj1 [0,-1,0,-337,-6719] 1 [85:756:1]&[29:84:1]
81312bk (1 curve)	0	2- 3- 7+ 11-	2- 3- -1 7+ 11-  4  5 -2
Curve Equation t 81312bk1 [0,1,0,-19741,1061003] 1
81312bl (4 curves)	0	2- 3- 7+ 11-	2- 3-  2 7+ 11- -2  2 -8
Curve Equation t 81312bl1 [0,1,0,-9962,-146280] 4 81312bl2 [0,1,0,36623,-1087297] 4 81312bl3 [0,1,0,-86192,9611160] 2 81312bl4 [0,1,0,-129752,-18018948] 2
81312bm (1 curve)	0	2- 3- 7+ 11-	2- 3- -2 7+ 11-  1  6  0
Curve Equation t 81312bm1 [0,1,0,-7784,276252] 1
81312bn (4 curves)	0	2- 3- 7+ 11-	2- 3- -2 7+ 11-  2  2  4
Curve Equation t 81312bn1 [0,1,0,-6574,165416] 4 81312bn2 [0,1,0,13391,991967] 2 81312bn3 [0,1,0,-31984,-2060500] 2 81312bn4 [0,1,0,-99744,12091176] 4
81312bo (4 curves)	2	2- 3- 7+ 11-	2- 3- -2 7+ 11-  2 -2 -4
Curve Equation t Generators 81312bo1 [0,1,0,-18674,968856] 4 [-116:1260:1]&[66:168:1] 81312bo2 [0,1,0,-5969,2277471] 2 [51:1452:1]&[429:8880:1] 81312bo3 [0,1,0,-31984,-607048] 2 [-158:726:1]&[-37:726:1] 81312bo4 [0,1,0,-298184,62572860] 2 [1215:38670:1]&[22122:1142361:8]
81312bp (1 curve)	0	2- 3- 7+ 11-	2- 3-  3 7+ 11-  0  5  2
Curve Equation t 81312bp1 [0,1,0,-6189,-189477] 1
81312bq (1 curve)	2	2- 3- 7+ 11-	2- 3- -3 7+ 11- -3 -3 -6
Curve Equation t Generators 81312bq1 [0,1,0,-337,6719] 1 [-1:-84:1]&[-22:63:1]
81312br (2 curves)	0	2- 3- 7+ 11-	2- 3- -4 7+ 11-  2  0  4
Curve Equation t 81312br1 [0,1,0,25370,-2246356] 2 81312br2 [0,1,0,-182145,-23620401] 2
81312bs (2 curves)	0	2- 3- 7- 11+	2- 3-  0 7- 11+  2  6  6
Curve Equation t 81312bs1 [0,1,0,-587858,-173677704] 2 81312bs2 [0,1,0,-601168,-165414856] 2
81312bt (1 curve)	1	2- 3- 7- 11-	2- 3-  1 7- 11-  4 -5 -2
Curve Equation t Generators 81312bt1 [0,1,0,-1085,12747] 1 [1:108:1]
81312bu (4 curves)	1	2- 3- 7- 11-	2- 3-  2 7- 11-  2 -6  0
Curve Equation t Generators 81312bu1 [0,1,0,-72882,1305720] 4 [-132:2940:1] 81312bu2 [0,1,0,286488,10649340] 2 [5754:194205:8] 81312bu3 [0,1,0,-725072,-236613192] 2 [1954:76230:1] 81312bu4 [0,1,0,-873297,313307487] 2 [579:1452:1]
81312bv (4 curves)	1	2- 3- 7- 11-	2- 3- -2 7- 11- -2 -2  4
Curve Equation t Generators 81312bv1 [0,1,0,-391354,-94330744] 4 [733:3630:1] 81312bv2 [0,1,0,-332064,-123833448] 2 [1602:58806:1] 81312bv3 [0,1,0,-451249,-63604609] 4 [-367:7260:1] 81312bv4 [0,1,0,-6261064,-6032129380] 2 [107455:35214630:1]
81312bw (1 curve)	1	2- 3- 7- 11-	2- 3-  3 7- 11-  4  7 -6
Curve Equation t Generators 81312bw1 [0,1,0,-3549,71883] 1 [21:84:1]
81312bx (2 curves)	1	2- 3- 7- 11-	2- 3-  4 7- 11- -6  0 -2
Curve Equation t Generators 81312bx1 [0,1,0,1654,-35928] 2 [67774:972840:343] 81312bx2 [0,1,0,-11656,-381988] 2 [1354:12705:8]

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