Cremona's table of elliptic curves

2678 = 2 · 13 · 103

Field	Data	Notes
Atkin-Lehner	2- 13- 103+	Signs for the Atkin-Lehner involutions
Class	2678n	Isogeny class
Conductor	2678	Conductor
∏ cp	5	Product of Tamagawa factors cp
deg	480	Modular degree for the optimal curve
Δ	42848 = 25 · 13 · 103	Discriminant
Eigenvalues	2- -2  2 -3 -3 13-  5  4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-102,388]	[a1,a2,a3,a4,a6]
Generators	[6:-2:1]	Generators of the group modulo torsion
j	117433042273/42848	j-invariant
L	3.5672674577803	L(r)(E,1)/r!
Ω	3.5441021012606	Real period
R	0.20130726236761	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	21424v1 85696h1 24102p1 66950h1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2678n1

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	-3	-3	-	5	4	-8	4	2	-8	-2	-10	-2	-9	0	2	-11	-10	-3	4	0	-2	16

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Quadratic twists for elliptic curve 2678n1

-4	8	-3	5	13
21424v1	85696h1	24102p1	66950h1	34814d1

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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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