Cremona's table of elliptic curves

12600 = 2³ · 3² · 5² · 7

Class	r	Atkin-Lehner	Eigenvalues
12600a (2 curves)	1	2+ 3+ 5+ 7+	2+ 3+ 5+ 7+  2  2  2 -8
Curve Equation t Generators 12600a1 [0,0,0,-7950,266625] 2 [-80:625:1] 12600a2 [0,0,0,1425,857250] 2 [-65:700:1]
12600b (2 curves)	1	2+ 3+ 5+ 7+	2+ 3+ 5+ 7+ -6  6 -2  4
Curve Equation t Generators 12600b1 [0,0,0,-150,625] 2 [0:25:1] 12600b2 [0,0,0,225,3250] 2 [11:84:1]
12600c (2 curves)	0	2+ 3+ 5+ 7-	2+ 3+ 5+ 7-  2  2  6  0
Curve Equation t 12600c1 [0,0,0,450,-2375] 2 12600c2 [0,0,0,-2175,-20750] 2
12600d (2 curves)	0	2+ 3+ 5+ 7-	2+ 3+ 5+ 7-  2 -2 -6 -4
Curve Equation t 12600d1 [0,0,0,-1350,-30375] 2 12600d2 [0,0,0,-24975,-1518750] 2
12600e (2 curves)	0	2+ 3+ 5+ 7-	2+ 3+ 5+ 7-  2  6  2  4
Curve Equation t 12600e1 [0,0,0,-3640950,3026804625] 2 12600e2 [0,0,0,-60364575,180515027250] 2
12600f (1 curve)	0	2+ 3+ 5+ 7-	2+ 3+ 5+ 7- -4 -1  3 -6
Curve Equation t 12600f1 [0,0,0,-211875,-49381250] 1
12600g (2 curves)	0	2+ 3+ 5+ 7-	2+ 3+ 5+ 7- -4 -6 -4 -2
Curve Equation t 12600g1 [0,0,0,-6075,87750] 2 12600g2 [0,0,0,20925,654750] 2
12600h (2 curves)	0	2+ 3+ 5- 7+	2+ 3+ 5- 7+ -2  2 -6 -4
Curve Equation t 12600h1 [0,0,0,-1755,-28250] 2 12600h2 [0,0,0,-2355,-7250] 2
12600i (1 curve)	0	2+ 3+ 5- 7+	2+ 3+ 5- 7+  4  1  3 -6
Curve Equation t 12600i1 [0,0,0,-76275,10666350] 1
12600j (2 curves)	1	2+ 3+ 5- 7-	2+ 3+ 5- 7-  2 -2 -6 -4
Curve Equation t Generators 12600j1 [0,0,0,-394875,95343750] 2 [159:6048:1] 12600j2 [0,0,0,-529875,24468750] 2 [34:2548:1]
12600k (2 curves)	0	2+ 3- 5+ 7+	2+ 3- 5+ 7+  0  0 -2 -2
Curve Equation t 12600k1 [0,0,0,-75,13750] 2 12600k2 [0,0,0,-9075,328750] 2
12600l (4 curves)	0	2+ 3- 5+ 7+	2+ 3- 5+ 7+  0  2  6 -4
Curve Equation t 12600l1 [0,0,0,1950,273625] 2 12600l2 [0,0,0,-53175,4518250] 4 12600l3 [0,0,0,-147675,-15988250] 2 12600l4 [0,0,0,-840675,296680750] 2
12600m (4 curves)	0	2+ 3- 5+ 7+	2+ 3- 5+ 7+  0 -6 -2  4
Curve Equation t 12600m1 [0,0,0,-1650,-167375] 2 12600m2 [0,0,0,-56775,-5183750] 4 12600m3 [0,0,0,-907275,-332626250] 2 12600m4 [0,0,0,-88275,1210750] 2
12600n (1 curve)	0	2+ 3- 5+ 7+	2+ 3- 5+ 7+ -1  2 -4 -2
Curve Equation t 12600n1 [0,0,0,5625,-253125] 1
12600o (1 curve)	0	2+ 3- 5+ 7+	2+ 3- 5+ 7+  3  2  0  2
Curve Equation t 12600o1 [0,0,0,-255,-1685] 1
12600p (1 curve)	0	2+ 3- 5+ 7+	2+ 3- 5+ 7+  5  5 -7 -2
Curve Equation t 12600p1 [0,0,0,-92700,-11191500] 1
12600q (4 curves)	1	2+ 3- 5+ 7-	2+ 3- 5+ 7-  0  2  6 -4
Curve Equation t Generators 12600q1 [0,0,0,-1650,25625] 2 [-20:225:1] 12600q2 [0,0,0,-2775,-13750] 4 [-25:200:1] 12600q3 [0,0,0,-34275,-2439250] 2 [214:162:1] 12600q4 [0,0,0,10725,-108250] 2 [31:504:1]
12600r (4 curves)	1	2+ 3- 5+ 7-	2+ 3- 5+ 7-  0 -2  2  0
Curve Equation t Generators 12600r1 [0,0,0,-3450,-23375] 2 [-40:225:1] 12600r2 [0,0,0,-31575,2142250] 4 [-30:1750:1] 12600r3 [0,0,0,-504075,137749750] 2 [510:3650:1] 12600r4 [0,0,0,-9075,5134750] 2 [-1:2268:1]
12600s (4 curves)	1	2+ 3- 5+ 7-	2+ 3- 5+ 7-  0 -6 -2  4
Curve Equation t Generators 12600s1 [0,0,0,-6298050,6082423625] 2 [-1660:109375:1] 12600s2 [0,0,0,-7001175,4640314250] 4 [-1705:107800:1] 12600s3 [0,0,0,-45588675,-115019523250] 2 [-29390:429275:8] 12600s4 [0,0,0,20336325,32005151750] 2 [-905:113400:1]
12600t (1 curve)	1	2+ 3- 5+ 7-	2+ 3- 5+ 7- -1 -4  0  6
Curve Equation t Generators 12600t1 [0,0,0,-255,3715] 1 [-1:63:1]
12600u (1 curve)	1	2+ 3- 5+ 7-	2+ 3- 5+ 7- -3  0 -2 -8
Curve Equation t Generators 12600u1 [0,0,0,-75,-1465] 1 [19:63:1]
12600v (4 curves)	1	2+ 3- 5+ 7-	2+ 3- 5+ 7- -4  2 -6  0
Curve Equation t Generators 12600v1 [0,0,0,-71175,7308250] 2 [110:900:1] 12600v2 [0,0,0,-75675,6331750] 4 [-289:2016:1] 12600v3 [0,0,0,-390675,-88483250] 2 [-414:1516:1] 12600v4 [0,0,0,167325,38650750] 2 [230:9450:1]
12600w (1 curve)	1	2+ 3- 5+ 7-	2+ 3- 5+ 7-  5 -1  3 -6
Curve Equation t Generators 12600w1 [0,0,0,-300,-15500] 1 [30:50:1]
12600x (1 curve)	1	2+ 3- 5- 7+	2+ 3- 5- 7+  1 -1  3 -4
Curve Equation t Generators 12600x1 [0,0,0,1500,-537500] 1 [150:1750:1]
12600y (1 curve)	1	2+ 3- 5- 7+	2+ 3- 5- 7+  1  4 -2 -4
Curve Equation t Generators 12600y1 [0,0,0,-15375,-2213125] 1 [175:675:1]
12600z (1 curve)	1	2+ 3- 5- 7+	2+ 3- 5- 7+  1 -6 -7  1
Curve Equation t Generators 12600z1 [0,0,0,-37875,2848750] 1 [114:112:1]
12600ba (2 curves)	1	2+ 3- 5- 7+	2+ 3- 5- 7+ -2  2  0  2
Curve Equation t Generators 12600ba1 [0,0,0,-138855,19915450] 2 [210:130:1] 12600ba2 [0,0,0,-137955,20186350] 2 [-25:4860:1]
12600bb (2 curves)	1	2+ 3- 5- 7+	2+ 3- 5- 7+ -2  2  0 -6
Curve Equation t Generators 12600bb1 [0,0,0,-6375,-143750] 2 [299:4968:1] 12600bb2 [0,0,0,16125,-931250] 2 [71:756:1]
12600bc (1 curve)	1	2+ 3- 5- 7+	2+ 3- 5- 7+ -2 -3  5  4
Curve Equation t Generators 12600bc1 [0,0,0,44476125,-198765301250] 1 [255337827809722012306:62270745819773624295732:4344231454155809]
12600bd (1 curve)	1	2+ 3- 5- 7+	2+ 3- 5- 7+  5  4 -2  4
Curve Equation t Generators 12600bd1 [0,0,0,-2775,56275] 1 [35:45:1]
12600be (1 curve)	1	2+ 3- 5- 7+	2+ 3- 5- 7+ -5  0  8 -2
Curve Equation t Generators 12600be1 [0,0,0,-75,-425] 1 [11:9:1]
12600bf (1 curve)	0	2+ 3- 5- 7-	2+ 3- 5- 7-  2 -5  3 -8
Curve Equation t 12600bf1 [0,0,0,-1875,-171250] 1
12600bg (1 curve)	0	2+ 3- 5- 7-	2+ 3- 5- 7-  3  2  4 -2
Curve Equation t 12600bg1 [0,0,0,142125,-27160625] 1
12600bh (1 curve)	0	2+ 3- 5- 7-	2+ 3- 5- 7- -5  2 -4  6
Curve Equation t 12600bh1 [0,0,0,-304275,64641575] 1
12600bi (2 curves)	0	2- 3+ 5+ 7+	2- 3+ 5+ 7+ -2  2 -2 -8
Curve Equation t 12600bi1 [0,0,0,-71550,-7198875] 2 12600bi2 [0,0,0,12825,-23145750] 2
12600bj (2 curves)	0	2- 3+ 5+ 7+	2- 3+ 5+ 7+  6  6  2  4
Curve Equation t 12600bj1 [0,0,0,-1350,-16875] 2 12600bj2 [0,0,0,2025,-87750] 2
12600bk (2 curves)	1	2- 3+ 5+ 7-	2- 3+ 5+ 7- -2  2 -6  0
Curve Equation t Generators 12600bk1 [0,0,0,4050,64125] 2 [10:325:1] 12600bk2 [0,0,0,-19575,560250] 2 [-95:1250:1]
12600bl (2 curves)	1	2- 3+ 5+ 7-	2- 3+ 5+ 7- -2 -2  6 -4
Curve Equation t Generators 12600bl1 [0,0,0,-150,1125] 2 [6:21:1] 12600bl2 [0,0,0,-2775,56250] 2 [25:50:1]
12600bm (2 curves)	1	2- 3+ 5+ 7-	2- 3+ 5+ 7- -2  6 -2  4
Curve Equation t Generators 12600bm1 [0,0,0,-404550,-112103875] 2 [1774:68943:1] 12600bm2 [0,0,0,-6707175,-6685741750] 2 [-1495:350:1]
12600bn (1 curve)	1	2- 3+ 5+ 7-	2- 3+ 5+ 7-  4 -1 -3 -6
Curve Equation t Generators 12600bn1 [0,0,0,-1906875,1333293750] 1 [894:18522:1]
12600bo (2 curves)	1	2- 3+ 5+ 7-	2- 3+ 5+ 7-  4 -6  4 -2
Curve Equation t Generators 12600bo1 [0,0,0,-675,-3250] 2 [-10:50:1] 12600bo2 [0,0,0,2325,-24250] 2 [110:1250:1]
12600bp (2 curves)	1	2- 3+ 5- 7+	2- 3+ 5- 7+  2  2  6 -4
Curve Equation t Generators 12600bp1 [0,0,0,-15795,762750] 2 [-141:432:1] 12600bp2 [0,0,0,-21195,195750] 2 [-146:422:1]
12600bq (1 curve)	1	2- 3+ 5- 7+	2- 3+ 5- 7+ -4  1 -3 -6
Curve Equation t Generators 12600bq1 [0,0,0,-8475,-395050] 1 [8734:816198:1]
12600br (2 curves)	0	2- 3+ 5- 7-	2- 3+ 5- 7- -2 -2  6 -4
Curve Equation t 12600br1 [0,0,0,-43875,-3531250] 2 12600br2 [0,0,0,-58875,-906250] 2
12600bs (4 curves)	1	2- 3- 5+ 7+	2- 3- 5+ 7+  0 -2  2  4
Curve Equation t Generators 12600bs1 [0,0,0,-8175,283250] 4 [-95:450:1] 12600bs2 [0,0,0,-12675,-63250] 4 [-101:432:1] 12600bs3 [0,0,0,-147675,-21798250] 2 [-226:182:1] 12600bs4 [0,0,0,50325,-504250] 2 [2510:126250:1]
12600bt (1 curve)	1	2- 3- 5+ 7+	2- 3- 5+ 7+  2  5 -3 -8
Curve Equation t Generators 12600bt1 [0,0,0,-75,-1370] 1 [14:18:1]
12600bu (1 curve)	1	2- 3- 5+ 7+	2- 3- 5+ 7+  3 -2 -4 -2
Curve Equation t Generators 12600bu1 [0,0,0,5685,-217285] 1 [49:423:1]
12600bv (4 curves)	1	2- 3- 5+ 7+	2- 3- 5+ 7+  4 -2 -2  0
Curve Equation t Generators 12600bv1 [0,0,0,1950,-9875] 2 [30:275:1] 12600bv2 [0,0,0,-8175,-80750] 4 [-55:450:1] 12600bv3 [0,0,0,-102675,-12649250] 2 [-181:72:1] 12600bv4 [0,0,0,-75675,7951750] 2 [219:1372:1]
12600bw (6 curves)	1	2- 3- 5+ 7+	2- 3- 5+ 7+ -4  2 -6  4
Curve Equation t Generators 12600bw1 [0,0,0,-165450,-25902875] 2 [1790:73575:1] 12600bw2 [0,0,0,-166575,-25532750] 4 [-259:486:1] 12600bw3 [0,0,0,-387075,56272750] 4 [7091:594864:1] 12600bw4 [0,0,0,35925,-83650250] 2 [491:7236:1] 12600bw5 [0,0,0,-5490075,4950049750] 2 [57778:4678587:8] 12600bw6 [0,0,0,1187925,398047750] 2 [-23610:3528775:216]
12600bx (1 curve)	1	2- 3- 5+ 7+	2- 3- 5+ 7+ -5 -2  4  6
Curve Equation t Generators 12600bx1 [0,0,0,-7606875,8080196875] 1 [1469:8703:1]
12600by (1 curve)	0	2- 3- 5+ 7-	2- 3- 5+ 7-  1 -4  2 -4
Curve Equation t 12600by1 [0,0,0,-615,-17705] 1
12600bz (1 curve)	0	2- 3- 5+ 7-	2- 3- 5+ 7-  1  6  7  1
Curve Equation t 12600bz1 [0,0,0,-1515,22790] 1
12600ca (1 curve)	0	2- 3- 5+ 7-	2- 3- 5+ 7- -2  3 -5  4
Curve Equation t 12600ca1 [0,0,0,1779045,-1590122410] 1
12600cb (6 curves)	0	2- 3- 5+ 7-	2- 3- 5+ 7-  4  2  2 -4
Curve Equation t 12600cb1 [0,0,0,-39450,-3015875] 2 12600cb2 [0,0,0,-40575,-2834750] 4 12600cb3 [0,0,0,-153075,20002750] 4 12600cb4 [0,0,0,53925,-14080250] 2 12600cb5 [0,0,0,-2358075,1393717750] 2 12600cb6 [0,0,0,251925,107887750] 2
12600cc (4 curves)	0	2- 3- 5+ 7-	2- 3- 5+ 7-  4 -2 -6  8
Curve Equation t 12600cc1 [0,0,0,225,-6750] 2 12600cc2 [0,0,0,-4275,-101250] 4 12600cc3 [0,0,0,-67275,-6716250] 2 12600cc4 [0,0,0,-13275,465750] 2
12600cd (4 curves)	0	2- 3- 5+ 7-	2- 3- 5+ 7-  4  6 -2 -8
Curve Equation t 12600cd1 [0,0,0,-16050,750125] 2 12600cd2 [0,0,0,-44175,-2596750] 4 12600cd3 [0,0,0,-651675,-202464250] 2 12600cd4 [0,0,0,113325,-16929250] 2
12600ce (6 curves)	0	2- 3- 5+ 7-	2- 3- 5+ 7- -4  2  2  4
Curve Equation t 12600ce1 [0,0,0,-3450,-320875] 2 12600ce2 [0,0,0,-94575,-11164750] 4 12600ce3 [0,0,0,-1512075,-715662250] 2 12600ce4 [0,0,0,-135075,-675250] 4 12600ce5 [0,0,0,-1458075,675377750] 2 12600ce6 [0,0,0,539925,-5400250] 2
12600cf (1 curve)	0	2- 3- 5+ 7-	2- 3- 5+ 7-  5 -4  2  4
Curve Equation t 12600cf1 [0,0,0,-69375,7034375] 1
12600cg (1 curve)	0	2- 3- 5+ 7-	2- 3- 5+ 7- -5  0 -8 -2
Curve Equation t 12600cg1 [0,0,0,-1875,-53125] 1
12600ch (1 curve)	0	2- 3- 5- 7+	2- 3- 5- 7+ -1  4  0  6
Curve Equation t 12600ch1 [0,0,0,-6375,464375] 1
12600ci (1 curve)	0	2- 3- 5- 7+	2- 3- 5- 7+ -3  0  2 -8
Curve Equation t 12600ci1 [0,0,0,-1875,-183125] 1
12600cj (1 curve)	1	2- 3- 5- 7-	2- 3- 5- 7-  1  1 -3 -4
Curve Equation t Generators 12600cj1 [0,0,0,60,-4300] 1 [20:70:1]
12600ck (1 curve)	1	2- 3- 5- 7-	2- 3- 5- 7- -1 -2  4 -2
Curve Equation t Generators 12600ck1 [0,0,0,225,-2025] 1 [45:-315:1]
12600cl (2 curves)	1	2- 3- 5- 7-	2- 3- 5- 7- -2 -2  0  2
Curve Equation t Generators 12600cl1 [0,0,0,-3471375,2489431250] 2 [1825:47250:1] 12600cl2 [0,0,0,-3448875,2523293750] 2 [475:31500:1]
12600cm (2 curves)	1	2- 3- 5- 7-	2- 3- 5- 7- -2 -2  0 -6
Curve Equation t Generators 12600cm1 [0,0,0,-255,-1150] 2 [-11:18:1] 12600cm2 [0,0,0,645,-7450] 2 [19:108:1]
12600cn (1 curve)	1	2- 3- 5- 7-	2- 3- 5- 7-  3 -2  0  2
Curve Equation t Generators 12600cn1 [0,0,0,-6375,-210625] 1 [421:8469:1]

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