Cremona's table of elliptic curves

1312 = 2⁵ · 41

Field	Data	Notes
Atkin-Lehner	2+ 41+	Signs for the Atkin-Lehner involutions
Class	1312a	Isogeny class
Conductor	1312	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	860672 = 29 · 412	Discriminant
Eigenvalues	2+  2 -2  0 -6 -4  6  2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-24,20]	[a1,a2,a3,a4,a6]
Generators	[-4:6:1]	Generators of the group modulo torsion
j	3112136/1681	j-invariant
L	3.1120155361439	L(r)(E,1)/r!
Ω	2.4548433982939	Real period
R	1.2677043017517	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	1312b2 2624f2 11808n2 32800k2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1312a2

a2	a3	a5	a7	a11	a13	a17	a19	a23	a29	a31	a37	a41	a43	a47	a53	a59	a61	a67	a71	a73	a79	a83	a89	a97
+	2	-2	0	-6	-4	6	2	0	-8	-8	2	+	8	0	-12	-4	-6	10	12	10	-8	8	-6	-2

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Quadratic twists for elliptic curve 1312a2

-4	8	-3	5	-7	41
1312b2	2624f2	11808n2	32800k2	64288j2	53792d2

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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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