Cremona's table of elliptic curves

49600 = 2⁶ · 5² · 31

Class	r	Atkin-Lehner	Eigenvalues
49600a (4 curves)	1	2+ 5+ 31+	2+  0 5+  0  0  2  6 -4
Curve Equation t Generators 49600a1 [0,0,0,-1100,70000] 2 [40:300:1] 49600a2 [0,0,0,-33100,2310000] 4 [-179:1581:1] 49600a3 [0,0,0,-49100,-154000] 2 [-933827:-7469853:4913] 49600a4 [0,0,0,-529100,148134000] 2 [3021:161619:1]
49600b (1 curve)	1	2+ 5+ 31+	2+  0 5+  1  5 -5 -2  2
Curve Equation t Generators 49600b1 [0,0,0,-7660,258480] 1 [54:48:1]
49600c (2 curves)	1	2+ 5+ 31+	2+  0 5+  2  4 -4  0  0
Curve Equation t Generators 49600c1 [0,0,0,-105200,13129000] 2 [-66:4448:1] 49600c2 [0,0,0,-120700,9006000] 2 [-39992:2169651:512]
49600d (2 curves)	1	2+ 5+ 31+	2+  0 5+  2 -4  0  0  4
Curve Equation t Generators 49600d1 [0,0,0,-1075,-13500] 2 [-9272:2739:512] 49600d2 [0,0,0,-1700,4000] 2 [-24:176:1]
49600e (1 curve)	1	2+ 5+ 31+	2+  0 5+ -3 -6 -4  0  5
Curve Equation t Generators 49600e1 [0,0,0,-1700,-27000] 1 [30947:255319:343]
49600f (1 curve)	1	2+ 5+ 31+	2+  0 5+  5 -5 -7 -6  6
Curve Equation t Generators 49600f1 [0,0,0,-227500,-46050000] 1 [1567820842:30944326656:2048383]
49600g (1 curve)	1	2+ 5+ 31+	2+ -1 5+  0  1  0  1  7
Curve Equation t Generators 49600g1 [0,-1,0,-1953,93217] 1 [31:248:1]
49600h (1 curve)	1	2+ 5+ 31+	2+ -1 5+  0  4 -6 -5  1
Curve Equation t Generators 49600h1 [0,-1,0,-133,887] 1 [2:25:1]
49600i (1 curve)	1	2+ 5+ 31+	2+ -1 5+ -2  2 -2  5 -1
Curve Equation t Generators 49600i1 [0,-1,0,-2533,69437] 1 [52:275:1]
49600j (2 curves)	1	2+ 5+ 31+	2+  2 5+  0 -2  0 -2  4
Curve Equation t Generators 49600j1 [0,-1,0,-105633,-13616863] 2 [474163771191:1135957397500:1249243533] 49600j2 [0,-1,0,-1705633,-856816863] 2 [202783251887968894179:-71789250776422029017300:1617806603297457]
49600k (2 curves)	1	2+ 5+ 31+	2+  2 5+  4 -4  4 -4 -4
Curve Equation t Generators 49600k1 [0,-1,0,-3133,-9363] 2 [-39:228:1] 49600k2 [0,-1,0,12367,-86863] 2 [1272:20881:27]
49600l (2 curves)	1	2+ 5+ 31+	2+ -2 5+  0 -2  4 -6 -4
Curve Equation t Generators 49600l1 [0,1,0,767,-2337] 2 [13:100:1] 49600l2 [0,1,0,-3233,-22337] 2 [-38:217:1]
49600m (1 curve)	1	2+ 5+ 31+	2+ -2 5+  3  2 -2  6 -1
Curve Equation t Generators 49600m1 [0,1,0,-33,1063] 1 [34:201:1]
49600n (1 curve)	1	2+ 5+ 31+	2+  3 5+ -2  2 -2  1 -1
Curve Equation t Generators 49600n1 [0,0,0,-3845200,-2902204000] 1 [109970444183745002293313696993435617446907267924251527293946355:12058291654124005980748048125968625335490662892677659106200227025:8901988670590433701272551230870712914922583139936597338363]
49600o (1 curve)	1	2+ 5+ 31+	2+ -3 5+  2 -2  2  3  3
Curve Equation t Generators 49600o1 [0,0,0,800,4000] 1 [65:575:1]
49600p (1 curve)	1	2+ 5+ 31+	2+ -3 5+  4  3 -4 -3  1
Curve Equation t Generators 49600p1 [0,0,0,12500,-650000] 1 [264:4588:1]
49600q (2 curves)	0	2+ 5+ 31-	2+  0 5+  0 -2  2  0  8
Curve Equation t 49600q1 [0,0,0,-32300,2478000] 2 49600q2 [0,0,0,-532300,149478000] 2
49600r (4 curves)	0	2+ 5+ 31-	2+  0 5+  0  4  2 -6 -4
Curve Equation t 49600r1 [0,0,0,-36200,-1659000] 2 49600r2 [0,0,0,-516700,-142926000] 4 49600r3 [0,0,0,-454700,-178514000] 2 49600r4 [0,0,0,-8266700,-9148426000] 2
49600s (2 curves)	0	2+ 5+ 31-	2+  0 5+ -2  4  0  0 -4
Curve Equation t 49600s1 [0,0,0,-1075,13500] 2 49600s2 [0,0,0,-1700,-4000] 2
49600t (1 curve)	0	2+ 5+ 31-	2+  0 5+  3 -2 -4  0 -1
Curve Equation t 49600t1 [0,0,0,100,-1000] 1
49600u (2 curves)	0	2+ 5+ 31-	2+  1 5+  4  0  2  3  7
Curve Equation t 49600u1 [0,1,0,-10133,389363] 1 49600u2 [0,1,0,5867,1477363] 1
49600v (1 curve)	0	2+ 5+ 31-	2+ -1 5+  0  0 -2 -3 -1
Curve Equation t 49600v1 [0,-1,0,-720133,-236875363] 1
49600w (2 curves)	0	2+ 5+ 31-	2+ -1 5+  2 -2 -6  7  5
Curve Equation t 49600w1 [0,-1,0,967,9187] 1 49600w2 [0,-1,0,-84033,-9365813] 1
49600x (2 curves)	0	2+ 5+ 31-	2+  2 5+  0  0  4  0 -4
Curve Equation t 49600x1 [0,-1,0,367,21137] 2 49600x2 [0,-1,0,-9633,351137] 2
49600y (2 curves)	0	2+ 5+ 31-	2+  2 5+ -4 -4  0  8 -4
Curve Equation t 49600y1 [0,-1,0,-1633,-88863] 2 49600y2 [0,-1,0,-41633,-3248863] 2
49600z (2 curves)	0	2+ 5+ 31-	2+ -2 5+  1  6  2 -6  1
Curve Equation t 49600z1 [0,1,0,-233,1663] 1 49600z2 [0,1,0,1767,-16337] 1
49600ba (4 curves)	0	2+ 5+ 31-	2+ -2 5+  4  0 -4  0  4
Curve Equation t 49600ba1 [0,1,0,-169633,27388863] 2 49600ba2 [0,1,0,-2729633,1734908863] 2 49600ba3 [0,1,0,726367,117884863] 2 49600ba4 [0,1,0,-3273633,993884863] 2
49600bb (1 curve)	0	2+ 5+ 31-	2+  3 5+ -4 -3 -4 -3 -1
Curve Equation t 49600bb1 [0,0,0,12500,650000] 1
49600bc (1 curve)	0	2+ 5- 31+	2+  0 5- -1  5  5  2  2
Curve Equation t 49600bc1 [0,0,0,-191500,32310000] 1
49600bd (1 curve)	0	2+ 5- 31+	2+  0 5- -5 -5  7  6  6
Curve Equation t 49600bd1 [0,0,0,-9100,-368400] 1
49600be (1 curve)	0	2+ 5- 31+	2+  1 5-  0  1  0 -1  7
Curve Equation t 49600be1 [0,1,0,-48833,11554463] 1
49600bf (1 curve)	0	2+ 5- 31+	2+  3 5- -4  3  4  3  1
Curve Equation t 49600bf1 [0,0,0,500,-5200] 1
49600bg (2 curves)	1	2+ 5- 31-	2+  2 5-  4 -4 -2  6 -4
Curve Equation t Generators 49600bg1 [0,-1,0,-213,-1003] 2 [-276:35:27] 49600bg2 [0,-1,0,-3313,-72303] 2 [8787:823620:1]
49600bh (2 curves)	1	2+ 5- 31-	2+ -2 5- -4 -4  2 -6 -4
Curve Equation t Generators 49600bh1 [0,1,0,-5333,-136037] 2 [-42:125:1] 49600bh2 [0,1,0,-82833,-9203537] 2 [-166:1:1]
49600bi (1 curve)	1	2+ 5- 31-	2+ -3 5-  4 -3  4  3 -1
Curve Equation t Generators 49600bi1 [0,0,0,500,5200] 1 [34:248:1]
49600bj (2 curves)	0	2- 5+ 31+	2-  0 5+  0  2  2  0 -8
Curve Equation t 49600bj1 [0,0,0,-32300,-2478000] 2 49600bj2 [0,0,0,-532300,-149478000] 2
49600bk (4 curves)	0	2- 5+ 31+	2-  0 5+  0 -4  2 -6  4
Curve Equation t 49600bk1 [0,0,0,-36200,1659000] 2 49600bk2 [0,0,0,-516700,142926000] 4 49600bk3 [0,0,0,-454700,178514000] 2 49600bk4 [0,0,0,-8266700,9148426000] 2
49600bl (1 curve)	0	2- 5+ 31+	2-  0 5+  1 -3  3  2  2
Curve Equation t 49600bl1 [0,0,0,20,-240] 1
49600bm (1 curve)	0	2- 5+ 31+	2-  0 5+ -3  2 -4  0  1
Curve Equation t 49600bm1 [0,0,0,100,1000] 1
49600bn (2 curves)	0	2- 5+ 31+	2-  0 5+  4  2 -6  4  4
Curve Equation t 49600bn1 [0,0,0,700,8000] 2 49600bn2 [0,0,0,-4300,78000] 2
49600bo (1 curve)	0	2- 5+ 31+	2-  1 5+  0  0 -2 -3  1
Curve Equation t 49600bo1 [0,1,0,-720133,236875363] 1
49600bp (2 curves)	0	2- 5+ 31+	2-  1 5+ -2  2 -6  7 -5
Curve Equation t 49600bp1 [0,1,0,967,-9187] 1 49600bp2 [0,1,0,-84033,9365813] 1
49600bq (2 curves)	0	2- 5+ 31+	2- -1 5+ -4  0  2  3 -7
Curve Equation t 49600bq1 [0,-1,0,-10133,-389363] 1 49600bq2 [0,-1,0,5867,-1477363] 1
49600br (2 curves)	0	2- 5+ 31+	2-  2 5+  0  6 -4 -2 -8
Curve Equation t 49600br1 [0,-1,0,-633,54137] 2 49600br2 [0,-1,0,-25633,1579137] 2
49600bs (2 curves)	0	2- 5+ 31+	2-  2 5+ -1 -6  2 -6 -1
Curve Equation t 49600bs1 [0,-1,0,-233,-1663] 1 49600bs2 [0,-1,0,1767,16337] 1
49600bt (4 curves)	0	2- 5+ 31+	2-  2 5+ -4  0 -4  0 -4
Curve Equation t 49600bt1 [0,-1,0,-169633,-27388863] 2 49600bt2 [0,-1,0,-2729633,-1734908863] 2 49600bt3 [0,-1,0,726367,-117884863] 2 49600bt4 [0,-1,0,-3273633,-993884863] 2
49600bu (2 curves)	0	2- 5+ 31+	2- -2 5+  0  0  4  0  4
Curve Equation t 49600bu1 [0,1,0,367,-21137] 2 49600bu2 [0,1,0,-9633,-351137] 2
49600bv (2 curves)	0	2- 5+ 31+	2- -2 5+  4  4  0  8  4
Curve Equation t 49600bv1 [0,1,0,-1633,88863] 2 49600bv2 [0,1,0,-41633,3248863] 2
49600bw (4 curves)	1	2- 5+ 31-	2-  0 5+  0  0  2  6  4
Curve Equation t Generators 49600bw1 [0,0,0,-1100,-70000] 2 [860:25200:1] 49600bw2 [0,0,0,-33100,-2310000] 4 [-75239710:-58867200:704969] 49600bw3 [0,0,0,-49100,154000] 2 [-1278:15841:8] 49600bw4 [0,0,0,-529100,-148134000] 2 [-6498625715652:-14381551953:15475479488]
49600bx (1 curve)	1	2- 5+ 31-	2-  0 5+ -1  3  3  2 -2
Curve Equation t Generators 49600bx1 [0,0,0,20,240] 1 [6:24:1]
49600by (1 curve)	1	2- 5+ 31-	2-  0 5+ -1 -5 -5 -2 -2
Curve Equation t Generators 49600by1 [0,0,0,-7660,-258480] 1 [154:1488:1]
49600bz (2 curves)	1	2- 5+ 31-	2-  0 5+ -2 -4 -4  0  0
Curve Equation t Generators 49600bz1 [0,0,0,-105200,-13129000] 2 [7910:702900:1] 49600bz2 [0,0,0,-120700,-9006000] 2 [390:1800:1]
49600ca (1 curve)	1	2- 5+ 31-	2-  0 5+  3  6 -4  0 -5
Curve Equation t Generators 49600ca1 [0,0,0,-1700,27000] 1 [-19:229:1]
49600cb (2 curves)	1	2- 5+ 31-	2-  0 5+ -4 -2 -6  4 -4
Curve Equation t Generators 49600cb1 [0,0,0,700,-8000] 2 [30:200:1] 49600cb2 [0,0,0,-4300,-78000] 2 [-51:93:1]
49600cc (1 curve)	1	2- 5+ 31-	2-  0 5+ -5  5 -7 -6 -6
Curve Equation t Generators 49600cc1 [0,0,0,-227500,46050000] 1 [-214:9216:1]
49600cd (1 curve)	1	2- 5+ 31-	2-  1 5+  0 -1  0  1 -7
Curve Equation t Generators 49600cd1 [0,1,0,-1953,-93217] 1 [7595:15872:125]
49600ce (1 curve)	1	2- 5+ 31-	2-  1 5+  0 -4 -6 -5 -1
Curve Equation t Generators 49600ce1 [0,1,0,-133,-887] 1 [48:325:1]
49600cf (1 curve)	1	2- 5+ 31-	2-  1 5+  2 -2 -2  5  1
Curve Equation t Generators 49600cf1 [0,1,0,-2533,-69437] 1 [13100646:93780775:148877]
49600cg (2 curves)	1	2- 5+ 31-	2-  2 5+  0  2  4 -6  4
Curve Equation t Generators 49600cg1 [0,-1,0,767,2337] 2 [717:19200:1] 49600cg2 [0,-1,0,-3233,22337] 2 [19389:517600:27]
49600ch (1 curve)	1	2- 5+ 31-	2-  2 5+ -3 -2 -2  6  1
Curve Equation t Generators 49600ch1 [0,-1,0,-33,-1063] 1 [340400:1404789:15625]
49600ci (2 curves)	1	2- 5+ 31-	2- -2 5+  0  2  0 -2 -4
Curve Equation t Generators 49600ci1 [0,1,0,-105633,13616863] 2 [-127:5000:1] 49600ci2 [0,1,0,-1705633,856816863] 2 [1153:20600:1]
49600cj (2 curves)	1	2- 5+ 31-	2- -2 5+  0 -6 -4 -2  8
Curve Equation t Generators 49600cj1 [0,1,0,-633,-54137] 2 [63:400:1] 49600cj2 [0,1,0,-25633,-1579137] 2 [313:4600:1]
49600ck (2 curves)	1	2- 5+ 31-	2- -2 5+ -4  4  4 -4  4
Curve Equation t Generators 49600ck1 [0,1,0,-3133,9363] 2 [-2:125:1] 49600ck2 [0,1,0,12367,86863] 2 [13:500:1]
49600cl (1 curve)	1	2- 5+ 31-	2-  3 5+ -2  2  2  3 -3
Curve Equation t Generators 49600cl1 [0,0,0,800,-4000] 1 [282555:2011375:19683]
49600cm (1 curve)	1	2- 5+ 31-	2- -3 5+  2 -2 -2  1  1
Curve Equation t Generators 49600cm1 [0,0,0,-3845200,2902204000] 1 [1065:3875:1]
49600cn (1 curve)	1	2- 5- 31+	2-  0 5- -1 -3 -3 -2  2
Curve Equation t Generators 49600cn1 [0,0,0,500,-30000] 1 [26:24:1]
49600co (1 curve)	1	2- 5- 31+	2-  1 5- -4 -6 -6  7  3
Curve Equation t Generators 49600co1 [0,1,0,-3,23] 1 [-2:5:1]
49600cp (1 curve)	1	2- 5- 31+	2- -1 5-  4 -6  6 -7  3
Curve Equation t Generators 49600cp1 [0,-1,0,-83,3037] 1 [92:875:1]
49600cq (2 curves)	1	2- 5- 31+	2-  2 5-  4  4  2 -6  4
Curve Equation t Generators 49600cq1 [0,-1,0,-5333,136037] 2 [40212:59489:729] 49600cq2 [0,-1,0,-82833,9203537] 2 [836779608:-76704551:5000211]
49600cr (2 curves)	1	2- 5- 31+	2- -2 5- -4  4 -2  6  4
Curve Equation t Generators 49600cr1 [0,1,0,-213,1003] 2 [3:20:1] 49600cr2 [0,1,0,-3313,72303] 2 [34:11:1]
49600cs (1 curve)	0	2- 5- 31-	2-  0 5-  1  3 -3 -2 -2
Curve Equation t 49600cs1 [0,0,0,500,30000] 1
49600ct (1 curve)	0	2- 5- 31-	2-  0 5-  1 -5  5  2 -2
Curve Equation t 49600ct1 [0,0,0,-191500,-32310000] 1
49600cu (1 curve)	0	2- 5- 31-	2-  0 5-  5  5  7  6 -6
Curve Equation t 49600cu1 [0,0,0,-9100,368400] 1
49600cv (1 curve)	0	2- 5- 31-	2-  1 5- -4  6  6 -7 -3
Curve Equation t 49600cv1 [0,1,0,-83,-3037] 1
49600cw (1 curve)	0	2- 5- 31-	2- -1 5-  0 -1  0 -1 -7
Curve Equation t 49600cw1 [0,-1,0,-48833,-11554463] 1
49600cx (1 curve)	0	2- 5- 31-	2- -1 5-  4  6 -6  7 -3
Curve Equation t 49600cx1 [0,-1,0,-3,-23] 1

Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
Back to Tables and computations