Cremona's table of elliptic curves

3135 = 3 · 5 · 11 · 19

Class	r	Atkin-Lehner	Eigenvalues
3135a (2 curves)	1	3+ 5+ 11- 19-	-1 3+ 5+ -4 11- -2 -4 19-
Curve Equation t Generators 3135a1 [1,1,1,-31,68] 2 [2:3:1] 3135a2 [1,1,1,-526,4424] 2 [8:24:1]
3135b (4 curves)	1	3+ 5- 11- 19+	-1 3+ 5-  0 11- -2 -2 19+
Curve Equation t Generators 3135b1 [1,1,1,120,120] 4 [24:120:1] 3135b2 [1,1,1,-485,362] 4 [-4:49:1] 3135b3 [1,1,1,-4940,-135070] 2 [-42:43:1] 3135b4 [1,1,1,-5710,163382] 2 [51:64:1]
3135c (1 curve)	1	3- 5+ 11+ 19-	2 3- 5+ -2 11+ -3 -3 19-
Curve Equation t Generators 3135c1 [0,1,1,14,-59] 1 [26:41:8]
3135d (2 curves)	0	3- 5+ 11- 19-	-1 3- 5+  4 11-  6  0 19-
Curve Equation t 3135d1 [1,0,0,-2756,-151305] 2 3135d2 [1,0,0,-62651,-6032994] 2
3135e (6 curves)	1	3- 5- 11+ 19+	-1 3- 5-  0 11+ -2  2 19+
Curve Equation t Generators 3135e1 [1,0,0,-980,11727] 4 [82:655:1] 3135e2 [1,0,0,-985,11600] 8 [-28:146:1] 3135e3 [1,0,0,-2110,-20125] 4 [70:385:1] 3135e4 [1,0,0,60,35217] 4 [-21:168:1] 3135e5 [1,0,0,-29185,-1920790] 2 [2726:40763:8] 3135e6 [1,0,0,6965,-145360] 2 [3028:32989:64]
3135f (4 curves)	0	3- 5- 11+ 19-	1 3- 5-  4 11+  2 -2 19-
Curve Equation t 3135f1 [1,0,1,-48,-119] 2 3135f2 [1,0,1,-173,731] 4 3135f3 [1,0,1,-2648,52211] 2 3135f4 [1,0,1,302,4151] 2
3135g (4 curves)	0	3- 5- 11- 19+	1 3- 5-  4 11-  2  6 19+
Curve Equation t 3135g1 [1,0,1,-23,173] 2 3135g2 [1,0,1,-628,5981] 4 3135g3 [1,0,1,-903,151] 2 3135g4 [1,0,1,-10033,385943] 2
3135h (2 curves)	0	3- 5- 11- 19+	-2 3- 5- -2 11- -1  3 19+
Curve Equation t 3135h1 [0,1,1,1770,-17494] 5 3135h2 [0,1,1,-285480,-58805794] 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
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