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	2678i	Isogeny class
Conductor	2678	Conductor
∏ cp	11	Product of Tamagawa factors cp
deg	1056	Modular degree for the optimal curve
Δ	2742272 = 211 · 13 · 103	Discriminant
Eigenvalues	2- -2 -4 -3 -5 13+ -3 -2	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-35,1]	[a1,a2,a3,a4,a6]
Generators	[-6:5:1] [-2:9:1]	Generators of the group modulo torsion
j	4750104241/2742272	j-invariant
L	3.3967016288332	L(r)(E,1)/r!
Ω	2.1700508941444	Real period
R	0.14229668898532	Regulator
r	2	Rank of the group of rational points
S	1.0000000000009	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	21424j1 85696w1 24102h1 66950n1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2678i1

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	-4	-3	-5	+	-3	-2	-6	-10	-4	-10	0	-4	2	1	14	-8	11	12	9	-4	-8	-10	14

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Quadratic twists for elliptic curve 2678i1

-4	8	-3	5	13
21424j1	85696w1	24102h1	66950n1	34814f1

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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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