Cremona's table of elliptic curves

42315 = 3 · 5 · 7 · 13 · 31

Class	r	Atkin-Lehner	Eigenvalues
42315a (2 curves)	1	3+ 5+ 7- 13+ 31-	-1 3+ 5+ 7-  2 13+  6 -8
Curve Equation t Generators 42315a1 [1,1,1,-126,474] 2 [-6:35:1] 42315a2 [1,1,1,-321,-1632] 2 [-9:29:1]
42315b (4 curves)	0	3+ 5- 7- 13+ 31-	1 3+ 5- 7-  4 13+ -2  4
Curve Equation t 42315b1 [1,1,0,-25482,1651959] 2 42315b2 [1,1,0,-414687,102611736] 4 42315b3 [1,1,0,-421662,98972181] 2 42315b4 [1,1,0,-6634992,6575461119] 2
42315c (6 curves)	0	3+ 5- 7- 13- 31+	-1 3+ 5- 7-  4 13-  2  4
Curve Equation t 42315c1 [1,1,1,-30855,2073252] 4 42315c2 [1,1,1,-30860,2072540] 8 42315c3 [1,1,1,-24815,2916422] 4 42315c4 [1,1,1,-36985,1183190] 4 42315c5 [1,1,1,131190,9121050] 2 42315c6 [1,1,1,-303160,-63550570] 2
42315d (4 curves)	1	3- 5+ 7+ 13+ 31-	-1 3- 5+ 7+  0 13+ -2 -4
Curve Equation t Generators 42315d1 [1,0,0,-9211,-340984] 2 [-55:29:1] 42315d2 [1,0,0,-10056,-274905] 4 [-57:366:1] 42315d3 [1,0,0,26799,-1815444] 2 [216:3642:1] 42315d4 [1,0,0,-60431,5498070] 2 [-167:3391:1]
42315e (4 curves)	0	3- 5+ 7+ 13- 31-	1 3- 5+ 7+  4 13- -6 -4
Curve Equation t 42315e1 [1,0,1,-109,-606709] 2 42315e2 [1,0,1,-108154,-13485673] 4 42315e3 [1,0,1,-222079,19825997] 2 42315e4 [1,0,1,-1722949,-870618859] 2
42315f (2 curves)	1	3- 5- 7+ 13+ 31+	-1 3- 5- 7+ -6 13+ -2  0
Curve Equation t Generators 42315f1 [1,0,0,-230,-525] 2 [-5:25:1] 42315f2 [1,0,0,-1985,33522] 2 [19:43:1]
42315g (4 curves)	1	3- 5- 7- 13+ 31-	1 3- 5- 7- -4 13+ -2  4
Curve Equation t Generators 42315g1 [1,0,1,447,-8057] 2 [77:657:1] 42315g2 [1,0,1,-4358,-96469] 4 [-330:1091:8] 42315g3 [1,0,1,-18463,868313] 2 [-71:1385:1] 42315g4 [1,0,1,-67133,-6700399] 2 [-1194:659:8]

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

Part of Computational Number Theory
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