Cremona's table of elliptic curves

312 = 2³ · 3 · 13

Class	r	Atkin-Lehner	Eigenvalues
312b (2 curves)	1	2+ 3+ 13+	2+ 3+  0 -4 -2 13+ -6 -4
Curve Equation t Generators 312b1 [0,-1,0,-3,0] 2 [-1:1:1] 312b2 [0,-1,0,12,-12] 2 [2:4:1]
312d (4 curves)	0	2+ 3+ 13-	2+ 3+ -2  4  0 13-  2  8
Curve Equation t 312d1 [0,-1,0,-39,108] 4 312d2 [0,-1,0,-44,84] 4 312d3 [0,-1,0,-304,-1892] 2 312d4 [0,-1,0,136,444] 4
312a (2 curves)	0	2+ 3- 13+	2+ 3-  0  0  6 13+  2  0
Curve Equation t 312a1 [0,1,0,-3,-6] 2 312a2 [0,1,0,-68,-240] 2
312e (2 curves)	0	2- 3+ 13+	2- 3+  4  0 -2 13+  2  8
Curve Equation t 312e1 [0,-1,0,-651,6228] 2 312e2 [0,-1,0,564,25668] 2
312f (2 curves)	1	2- 3- 13+	2- 3- -4 -4 -2 13+ -6  4
Curve Equation t Generators 312f1 [0,1,0,5,14] 2 [-1:3:1] 312f2 [0,1,0,-60,144] 2 [-6:18:1]
312c (4 curves)	0	2- 3- 13-	2- 3-  2  0  0 13-  2 -4
Curve Equation t 312c1 [0,1,0,-7,2] 4 312c2 [0,1,0,-52,-160] 4 312c3 [0,1,0,-832,-9520] 2 312c4 [0,1,0,8,-448] 2

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

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