Cremona's table of elliptic curves

12720 = 2⁴ · 3 · 5 · 53

Class	r	Atkin-Lehner	Eigenvalues
12720a (4 curves)	1	2+ 3+ 5+ 53+	2+ 3+ 5+  0 -4  2  2  4
Curve Equation t Generators 12720a1 [0,-1,0,-796,-8384] 2 [33:14:1] 12720a2 [0,-1,0,-816,-7920] 4 [-16:28:1] 12720a3 [0,-1,0,-2936,53136] 2 [-40:324:1] 12720a4 [0,-1,0,984,-39600] 2 [74:658:1]
12720b (2 curves)	1	2+ 3+ 5+ 53+	2+ 3+ 5+ -2  0  6  6 -6
Curve Equation t Generators 12720b1 [0,-1,0,-76,256] 2 [0:16:1] 12720b2 [0,-1,0,104,1120] 2 [-2:30:1]
12720c (2 curves)	0	2+ 3+ 5- 53+	2+ 3+ 5- -2  0  4  0  0
Curve Equation t 12720c1 [0,-1,0,-863102600,9760096560000] 2 12720c2 [0,-1,0,-870188480,9591696370272] 2
12720d (1 curve)	0	2+ 3+ 5- 53+	2+ 3+ 5- -2  0  4  7  0
Curve Equation t 12720d1 [0,-1,0,15,-3] 1
12720e (1 curve)	0	2+ 3+ 5- 53+	2+ 3+ 5-  3 -5 -6  0 -5
Curve Equation t 12720e1 [0,-1,0,-3360,-74208] 1
12720f (2 curves)	0	2+ 3+ 5- 53+	2+ 3+ 5-  4  4  4  0 -2
Curve Equation t 12720f1 [0,-1,0,-80,-240] 2 12720f2 [0,-1,0,40,-1008] 2
12720g (2 curves)	0	2+ 3+ 5- 53+	2+ 3+ 5-  4  6 -2  0  6
Curve Equation t 12720g1 [0,-1,0,40,0] 2 12720g2 [0,-1,0,-160,160] 2
12720h (2 curves)	1	2+ 3+ 5- 53-	2+ 3+ 5-  2  0 -2  2  6
Curve Equation t Generators 12720h1 [0,-1,0,-2100,-36000] 2 [-28:8:1] 12720h2 [0,-1,0,-480,-91728] 2 [102:954:1]
12720i (2 curves)	0	2+ 3- 5+ 53+	2+ 3- 5+  4  2  4  2 -4
Curve Equation t 12720i1 [0,1,0,-136,644] 2 12720i2 [0,1,0,-2256,40500] 2
12720j (4 curves)	0	2+ 3- 5+ 53+	2+ 3- 5+  4 -4  2 -6  0
Curve Equation t 12720j1 [0,1,0,-2316,-43380] 2 12720j2 [0,1,0,-3936,23364] 4 12720j3 [0,1,0,-48936,4145364] 2 12720j4 [0,1,0,15144,198900] 2
12720k (2 curves)	1	2+ 3- 5+ 53-	2+ 3- 5+ -2  0  0  0  0
Curve Equation t Generators 12720k1 [0,1,0,-96,324] 2 [0:18:1] 12720k2 [0,1,0,-216,-780] 2 [-4:6:1]
12720l (1 curve)	1	2+ 3- 5- 53+	2+ 3- 5- -5 -1  2  0 -3
Curve Equation t Generators 12720l1 [0,1,0,40,30900] 1 [10:180:1]
12720m (4 curves)	0	2- 3+ 5+ 53+	2- 3+ 5+  0  0 -2  2  4
Curve Equation t 12720m1 [0,-1,0,984,-3984] 2 12720m2 [0,-1,0,-4136,-28560] 4 12720m3 [0,-1,0,-52136,-4559760] 2 12720m4 [0,-1,0,-38056,2847856] 2
12720n (4 curves)	0	2- 3+ 5+ 53+	2- 3+ 5+  0 -4  6  6  0
Curve Equation t 12720n1 [0,-1,0,344,1456] 2 12720n2 [0,-1,0,-1656,14256] 4 12720n3 [0,-1,0,-12456,-521424] 2 12720n4 [0,-1,0,-22856,1337136] 2
12720o (2 curves)	0	2- 3+ 5+ 53+	2- 3+ 5+ -2  0 -4  3 -8
Curve Equation t 12720o1 [0,-1,0,-7861,-983939] 1 12720o2 [0,-1,0,69899,24863485] 1
12720p (1 curve)	0	2- 3+ 5+ 53+	2- 3+ 5+  3  3 -2 -4  7
Curve Equation t 12720p1 [0,-1,0,-6496,-231680] 1
12720q (1 curve)	1	2- 3+ 5+ 53-	2- 3+ 5+ -1  5  2 -4 -1
Curve Equation t Generators 12720q1 [0,-1,0,4133784,-2350563984] 1 [5906:477530:1]
12720r (2 curves)	1	2- 3+ 5+ 53-	2- 3+ 5+  2 -4 -4 -4 -4
Curve Equation t Generators 12720r1 [0,-1,0,-376,880] 2 [-4:48:1] 12720r2 [0,-1,0,-4696,125296] 2 [-12:424:1]
12720s (2 curves)	1	2- 3+ 5- 53+	2- 3+ 5-  0 -2  2  0  2
Curve Equation t Generators 12720s1 [0,-1,0,-160,1792] 2 [-6:50:1] 12720s2 [0,-1,0,-3360,76032] 2 [32:16:1]
12720t (2 curves)	1	2- 3+ 5- 53+	2- 3+ 5-  0  4 -4  0  2
Curve Equation t Generators 12720t1 [0,-1,0,-44840,2739312] 2 [4:1600:1] 12720t2 [0,-1,0,110680,17420400] 2 [130:5830:1]
12720u (4 curves)	1	2- 3+ 5- 53+	2- 3+ 5- -2  0 -4  0 -8
Curve Equation t Generators 12720u1 [0,-1,0,-3360,52992] 2 [-16:320:1] 12720u2 [0,-1,0,-20640,-1094400] 2 [-70:50:1] 12720u3 [0,-1,0,-248160,47665152] 2 [272:464:1] 12720u4 [0,-1,0,-248640,47472000] 2 [266:290:1]
12720v (2 curves)	1	2- 3- 5+ 53+	2- 3- 5+  0  2  4 -2 -4
Curve Equation t Generators 12720v1 [0,1,0,-1856,54324] 2 [10:192:1] 12720v2 [0,1,0,-35776,2591540] 2 [26:1296:1]
12720w (4 curves)	1	2- 3- 5+ 53+	2- 3- 5+  0 -4 -2 -2  8
Curve Equation t Generators 12720w1 [0,1,0,-251816,15133620] 2 [-524:1866:1] 12720w2 [0,1,0,-3200936,2201021364] 4 [97780:30570678:1] 12720w3 [0,1,0,-51200936,140997821364] 2 [210109650420:65562542985142:2146689] 12720w4 [0,1,0,-2386856,3348222900] 2 [-123666115436275692:1935875612441406250:64572901005159]
12720x (1 curve)	1	2- 3- 5+ 53+	2- 3- 5+  3 -1 -2  4 -7
Curve Equation t Generators 12720x1 [0,1,0,104,404] 1 [4:30:1]
12720y (2 curves)	1	2- 3- 5+ 53+	2- 3- 5+ -4 -2  0  2  4
Curve Equation t Generators 12720y1 [0,1,0,54944,9750644] 2 [-28:2862:1] 12720y2 [0,1,0,-487776,111130740] 2 [186:5184:1]
12720z (4 curves)	1	2- 3- 5+ 53+	2- 3- 5+ -4  4 -2 -2 -4
Curve Equation t Generators 12720z1 [0,1,0,-136,-460] 2 [-4:6:1] 12720z2 [0,1,0,-856,9044] 4 [-26:120:1] 12720z3 [0,1,0,-13576,604340] 2 [292:4650:1] 12720z4 [0,1,0,344,33524] 2 [-20:138:1]
12720ba (1 curve)	0	2- 3- 5+ 53-	2- 3- 5+ -1  1 -6 -4  1
Curve Equation t 12720ba1 [0,1,0,-1760336,-899574636] 1
12720bb (1 curve)	0	2- 3- 5+ 53-	2- 3- 5+  2  4  0  5  4
Curve Equation t 12720bb1 [0,1,0,-3541,80195] 1
12720bc (2 curves)	0	2- 3- 5+ 53-	2- 3- 5+ -2  0  0  8  0
Curve Equation t 12720bc1 [0,1,0,-165976,-26035180] 2 12720bc2 [0,1,0,-2654296,-1665340396] 2
12720bd (2 curves)	0	2- 3- 5+ 53-	2- 3- 5+  4 -4  4 -4  6
Curve Equation t 12720bd1 [0,1,0,-2176,38324] 2 12720bd2 [0,1,0,-1696,56180] 2
12720be (2 curves)	0	2- 3- 5+ 53-	2- 3- 5+  4  6  6 -4  6
Curve Equation t 12720be1 [0,1,0,5304,6552180] 2 12720be2 [0,1,0,-494696,130752180] 2
12720bf (2 curves)	0	2- 3- 5+ 53-	2- 3- 5+ -4 -2  6 -4 -2
Curve Equation t 12720bf1 [0,1,0,-13176,-658476] 2 12720bf2 [0,1,0,-217976,-39242796] 2
12720bg (2 curves)	0	2- 3- 5- 53+	2- 3- 5-  2  4  0 -4  4
Curve Equation t 12720bg1 [0,1,0,-2720,-49932] 2 12720bg2 [0,1,0,-10400,352500] 2
12720bh (4 curves)	1	2- 3- 5- 53-	2- 3- 5-  0  0 -2 -2 -8
Curve Equation t Generators 12720bh1 [0,1,0,-480,-5772] 2 [116:1230:1] 12720bh2 [0,1,0,-8480,-303372] 4 [3612:26650:27] 12720bh3 [0,1,0,-135680,-19281612] 2 [-32252220156:2997210:151419437] 12720bh4 [0,1,0,-9280,-243532] 4 [-62:312:1]
12720bi (1 curve)	1	2- 3- 5- 53-	2- 3- 5- -2 -4  4  5  0
Curve Equation t Generators 12720bi1 [0,1,0,-5,975] 1 [-5:30:1]
12720bj (4 curves)	1	2- 3- 5- 53-	2- 3- 5-  4 -4 -2  2  0
Curve Equation t Generators 12720bj1 [0,1,0,-14488960,-21232578892] 2 [10346:967680:1] 12720bj2 [0,1,0,-14490240,-21228641100] 4 [-2220:1890:1] 12720bj3 [0,1,0,-16610240,-14611697100] 4 [-3110:83520:1] 12720bj4 [0,1,0,-12390720,-27593545932] 4 [5391:249630:1]
12720bk (4 curves)	1	2- 3- 5- 53-	2- 3- 5- -4 -4  6 -6  0
Curve Equation t Generators 12720bk1 [0,1,0,-2160,-4140] 2 [-21:180:1] 12720bk2 [0,1,0,-22640,1298388] 4 [-68:1590:1] 12720bk3 [0,1,0,-361840,83656148] 4 [178:4992:1] 12720bk4 [0,1,0,-11120,2630100] 4 [460:9750:1]
12720bl (1 curve)	1	2- 3- 5- 53-	2- 3- 5- -5  5 -2  8 -3
Curve Equation t Generators 12720bl1 [0,1,0,-138698240,628669809588] 1 [6826:-3840:1]

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