Cremona's table of elliptic curves

676 = 2² · 13²

Field	Data	Notes
Atkin-Lehner	2- 13+	Signs for the Atkin-Lehner involutions
Class	676a	Isogeny class
Conductor	676	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	252	Modular degree for the optimal curve
Δ	1003976272 = 24 · 137	Discriminant
Eigenvalues	2-  0 -2  2  2 13+  6  6	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-676,-6591]	[a1,a2,a3,a4,a6]
j	442368/13	j-invariant
L	1.4069691052226	L(r)(E,1)/r!
Ω	0.93797940348175	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	2704f1 10816c1 6084i1 16900a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 676a1

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
-	0	-2	2	2	+	6	6	8	2	-10	6	6	4	2	6	10	-2	-10	-10	-2	-4	6	6	-2

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Quadratic twists for elliptic curve 676a1

-4	8	-3	5	-7	-11	13
2704f1	10816c1	6084i1	16900a1	33124h1	81796c1	52a2

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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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