Cremona's table of elliptic curves

67270 = 2 · 5 · 7 · 31²

Class	r	Atkin-Lehner	Eigenvalues
67270a (1 curve)	0	2+ 5+ 7+ 31-	2+  1 5+ 7+  3  3 -4 -7
Curve Equation t 67270a1 [1,0,1,-123509,2209792] 1
67270b (1 curve)	2	2+ 5+ 7+ 31-	2+ -1 5+ 7+ -3 -3  4 -7
Curve Equation t Generators 67270b1 [1,1,0,-128,-128] 1 [-66:203:8]&[-3:17:1]
67270c (2 curves)	2	2+ 5+ 7+ 31-	2+  2 5+ 7+  0 -6  4 -8
Curve Equation t Generators 67270c1 [1,1,0,11032,-331828] 2 [46:502:1]&[586:-14708:1] 67270c2 [1,1,0,-56238,-3036082] 2 [-127:1505:1]&[21423:563726:27]
67270d (1 curve)	0	2+ 5+ 7+ 31-	2+ -3 5+ 7+  5 -1  4 -3
Curve Equation t 67270d1 [1,-1,0,-17101360360,798392935825216] 1
67270e (2 curves)	0	2+ 5+ 7- 31+	2+ -2 5+ 7-  0  5 -3 -7
Curve Equation t 67270e1 [1,0,1,-225492424,1302307731222] 3 67270e2 [1,0,1,-787499639,-7082553803814] 1
67270f (1 curve)	1	2+ 5+ 7- 31-	2+  1 5+ 7- -3  5 -2  5
Curve Equation t Generators 67270f1 [1,0,1,-1369,-17558] 1 [-16:25:1]
67270g (1 curve)	1	2+ 5+ 7- 31-	2+ -1 5+ 7-  3 -5  2  5
Curve Equation t Generators 67270g1 [1,1,0,-1315148,519117502] 1 [6124459:400471761:1331]
67270h (3 curves)	1	2+ 5+ 7- 31-	2+ -1 5+ 7- -3 -5  6 -7
Curve Equation t Generators 67270h1 [1,1,0,-565568,-163945922] 1 [2601:125071:1] 67270h2 [1,1,0,-628033,-125583763] 1 [989:14401:1] 67270h3 [1,1,0,-20439048,35551551808] 1 [21366:27757:8]
67270i (2 curves)	1	2+ 5+ 7- 31-	2+  2 5+ 7-  0 -5  3 -7
Curve Equation t Generators 67270i1 [1,1,0,-234643,-43813203] 1 [-7422:6455:27] 67270i2 [1,1,0,-819458,237397748] 1 [7644:139538:27]
67270j (2 curves)	1	2+ 5- 7+ 31-	2+  0 5- 7+  2 -2 -6 -4
Curve Equation t Generators 67270j1 [1,-1,0,-2164,16848] 2 [-23:244:1] 67270j2 [1,-1,0,7756,122000] 2 [16:492:1]
67270k (2 curves)	1	2+ 5- 7+ 31-	2+  0 5- 7+ -2  2  6 -4
Curve Equation t Generators 67270k1 [1,-1,0,-2079784,-485280960] 2 [65296:-16713608:1] 67270k2 [1,-1,0,7453336,-3694129152] 2 [512:15744:1]
67270l (2 curves)	1	2+ 5- 7+ 31-	2+  2 5- 7+  0  0 -6  4
Curve Equation t Generators 67270l1 [1,1,0,-8882062,10245104436] 2 [-6622980:218987202:2197] 67270l2 [1,1,0,-142345742,653620120244] 2 [94722555447:-22646829899546:1601613]
67270m (2 curves)	1	2+ 5- 7+ 31-	2+ -2 5- 7+  0  0  6  4
Curve Equation t Generators 67270m1 [1,0,1,-9243,-344794] 2 [142:1029:1] 67270m2 [1,0,1,-148123,-21954522] 2 [1038:30188:1]
67270n (1 curve)	1	2+ 5- 7+ 31-	2+  3 5- 7+  5 -5  6 -1
Curve Equation t Generators 67270n1 [1,-1,0,-5207839,4575703493] 1 [2781113216889:-704704348510:2102071041]
67270o (1 curve)	1	2+ 5- 7+ 31-	2+ -3 5- 7+  1  1 -6  3
Curve Equation t Generators 67270o1 [1,-1,0,-119344,-15728672] 1 [-201:430:1]
67270p (1 curve)	1	2+ 5- 7+ 31-	2+ -3 5- 7+ -5  5 -6 -1
Curve Equation t Generators 67270p1 [1,-1,0,-5419,-152195] 1 [-338:171:8]
67270q (2 curves)	1	2+ 5- 7- 31+	2+ -2 5- 7-  0 -1  3 -1
Curve Equation t Generators 67270q1 [1,0,1,-2423,-25494] 3 [-25:152:1] 67270q2 [1,0,1,-170598,-27135304] 1 [-6441:3271:27]
67270r (1 curve)	0	2+ 5- 7- 31-	2+  1 5- 7- -1 -1  8  7
Curve Equation t 67270r1 [1,0,1,-84108,-8807112] 1
67270s (2 curves)	2	2+ 5- 7- 31-	2+ -1 5- 7- -3  1  0 -1
Curve Equation t Generators 67270s1 [1,1,0,-1386262,-628525996] 1 [-43468:-11901:64]&[-677:846:1] 67270s2 [1,1,0,-4245237,2613988909] 1 [-11724:-3718013:64]&[350:394051:8]
67270t (2 curves)	0	2+ 5- 7- 31-	2+  2 5- 7-  0  1 -3 -1
Curve Equation t 67270t1 [1,1,0,-2328042,752500196] 1 67270t2 [1,1,0,-163944217,807896001381] 1
67270u (4 curves)	0	2+ 5- 7- 31-	2+  2 5- 7-  0 -2  0 -4
Curve Equation t 67270u1 [1,1,0,6181613,-9210893139] 2 67270u2 [1,1,0,-46558067,-98309308531] 2 67270u3 [1,1,0,-58565762,332032494836] 2 67270u4 [1,1,0,-1160717442,15211741465844] 2
67270v (2 curves)	0	2+ 5- 7- 31-	2+ -2 5- 7-  0 -2 -4  4
Curve Equation t 67270v1 [1,0,1,-2423,2234778] 2 67270v2 [1,0,1,-271503,53790506] 2
67270w (2 curves)	1	2- 5+ 7+ 31-	2-  0 5+ 7+  2 -6  4  0
Curve Equation t Generators 67270w1 [1,-1,1,-1914973,-2190920219] 2 [26863:4383240:1] 67270w2 [1,-1,1,-39586173,-95781249499] 2 [1738452:277149445:64]
67270x (2 curves)	1	2- 5+ 7+ 31-	2-  0 5+ 7+ -4 -4 -2  0
Curve Equation t Generators 67270x1 [1,-1,1,429670127,-230026433919] 2 [115173:39653816:1] 67270x2 [1,-1,1,-1722969873,-1841062209919] 2 [-15399:4594552:1]
67270y (4 curves)	1	2- 5+ 7+ 31-	2-  0 5+ 7+ -4  6 -2  0
Curve Equation t Generators 67270y1 [1,-1,1,2222,63681] 2 [75:767:1] 67270y2 [1,-1,1,-16998,694097] 4 [39179:145839:343] 67270y3 [1,-1,1,-84268,-8777519] 2 [2263584330:-74464037353:2000376] 67270y4 [1,-1,1,-257248,50281697] 2 [1366:26221:8]
67270z (1 curve)	1	2- 5+ 7+ 31-	2-  1 5+ 7+ -1  1 -2 -3
Curve Equation t Generators 67270z1 [1,0,0,-83165921,289938209225] 1 [5846:56659:1]
67270ba (1 curve)	1	2- 5+ 7+ 31-	2- -1 5+ 7+  1 -1  2 -3
Curve Equation t Generators 67270ba1 [1,1,1,-86541,-9768701] 1 [-169:-172:1]
67270bb (2 curves)	1	2- 5+ 7+ 31-	2-  2 5+ 7+ -2 -4  8  0
Curve Equation t Generators 67270bb1 [1,1,1,-1389626,-632043977] 2 [101749020844551:2531133031931089:60282398961] 67270bb2 [1,1,1,-22243326,-40387537657] 2 [529775215761008180769595053:-60004057443610684109177394839:36669260025721639510137]
67270bc (2 curves)	1	2- 5+ 7+ 31-	2- -2 5+ 7+  2  4 -8  0
Curve Equation t Generators 67270bc1 [1,0,0,-1446,21076] 2 [18:22:1] 67270bc2 [1,0,0,-23146,1353456] 2 [88:-48:1]
67270bd (2 curves)	0	2- 5+ 7- 31-	2-  0 5+ 7- -2  2  0  8
Curve Equation t 67270bd1 [1,-1,1,-156343,24152107] 2 67270bd2 [1,-1,1,-2510793,1531941887] 2
67270be (1 curve)	0	2- 5+ 7- 31-	2- -1 5+ 7-  5  5  0  1
Curve Equation t 67270be1 [1,1,1,-5786,101823] 1
67270bf (2 curves)	0	2- 5+ 7- 31-	2-  2 5+ 7-  2 -4  6  4
Curve Equation t 67270bf1 [1,1,1,-2610096,-5262962671] 2 67270bf2 [1,1,1,-64114096,-197253849071] 2
67270bg (4 curves)	0	2- 5+ 7- 31-	2-  2 5+ 7- -6 -2  6 -4
Curve Equation t 67270bg1 [1,1,1,-121106,554345119] 2 67270bg2 [1,1,1,-10884306,13668227999] 2 67270bg3 [1,1,1,-54936546,156708757343] 2 67270bg4 [1,1,1,-878994046,10030236099343] 2
67270bh (2 curves)	0	2- 5- 7+ 31-	2-  0 5- 7+  2  4  6 -4
Curve Equation t 67270bh1 [1,-1,1,-366802,-109951599] 2 67270bh2 [1,-1,1,-6325002,-6120583759] 2
67270bi (2 curves)	2	2- 5- 7+ 31-	2-  0 5- 7+ -2 -4 -6 -4
Curve Equation t Generators 67270bi1 [1,-1,1,-382,3789] 2 [-21:57:1]&[-3:71:1] 67270bi2 [1,-1,1,-6582,207149] 2 [39:73:1]&[382:-141:8]
67270bj (1 curve)	0	2- 5- 7+ 31-	2-  3 5- 7+ -1  5  4  3
Curve Equation t 67270bj1 [1,-1,1,-270702,-53879171] 1
67270bk (1 curve)	0	2- 5- 7+ 31-	2-  3 5- 7+  5  1  0 -1
Curve Equation t 67270bk1 [1,-1,1,-2102121852,-16714986301121] 1
67270bl (1 curve)	2	2- 5- 7+ 31-	2- -3 5- 7+ -5 -1  0 -1
Curve Equation t Generators 67270bl1 [1,-1,1,-2187432,561639531] 1 [141:-16071:1]&[-1139:40249:1]
67270bm (1 curve)	0	2- 5- 7- 31+	2-  2 5- 7-  0  5  7 -5
Curve Equation t 67270bm1 [1,1,1,-168195,26396705] 1
67270bn (2 curves)	1	2- 5- 7- 31-	2-  1 5- 7-  3  1  2 -5
Curve Equation t Generators 67270bn1 [1,0,0,-9605215,4655241817] 1 [17874:-2363387:1] 67270bn2 [1,0,0,-4948568615,133988082366497] 1 [43232:901905:1]
67270bo (1 curve)	1	2- 5- 7- 31-	2- -2 5- 7-  0 -5 -7 -5
Curve Equation t Generators 67270bo1 [1,0,0,-175,-903] 1 [-8:5:1]
67270bp (2 curves)	1	2- 5- 7- 31-	2- -2 5- 7- -6  0  6  0
Curve Equation t Generators 67270bp1 [1,0,0,14395,2714077] 2 [-538:9879:8] 67270bp2 [1,0,0,-225855,38319127] 2 [9382:293219:8]

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