Cremona's table of elliptic curves

676 = 2² · 13²

Field	Data	Notes
Atkin-Lehner	2- 13+	Signs for the Atkin-Lehner involutions
Class	676c	Isogeny class
Conductor	676	Conductor
∏ cp	9	Product of Tamagawa factors cp
deg	780	Modular degree for the optimal curve
Δ	-208827064576 = -1 · 28 · 138	Discriminant
Eigenvalues	2- -2 -3 -4  0 13+  3  2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-732,-23516]	[a1,a2,a3,a4,a6]
j	-208	j-invariant
L	0.41506603837086	L(r)(E,1)/r!
Ω	0.41506603837086	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	2704i1 10816l1 6084l1 16900k1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 676c1

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	-3	-4	0	+	3	2	-6	9	2	-7	3	-4	-6	9	0	5	2	-6	-1	-4	12	6	14

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Quadratic twists for elliptic curve 676c1

-4	8	-3	5	-7	-11	13
2704i1	10816l1	6084l1	16900k1	33124q1	81796q1	676b1

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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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