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	3	Product of Tamagawa factors cp
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,-88612,-10182444]	[a1,a2,a3,a4,a6]
j	-368484688	j-invariant
L	0.41506603837086	L(r)(E,1)/r!
Ω	0.13835534612362	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	2704i2 10816l2 6084l2 16900k2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 676c2

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 676c2

-4	8	-3	5	-7	-11	13
2704i2	10816l2	6084l2	16900k2	33124q2	81796q2	676b2

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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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