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	2678h	Isogeny class
Conductor	2678	Conductor
∏ cp	9	Product of Tamagawa factors cp
Δ	78666832904192 = 215 · 133 · 1033	Discriminant
Eigenvalues	2+ -2  0 -1  3 13- -3  2	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-31421,2098200]	[a1,a2,a3,a4,a6]
Generators	[114:-25:1]	Generators of the group modulo torsion
j	3430550772360231625/78666832904192	j-invariant
L	1.6797127147276	L(r)(E,1)/r!
Ω	0.60955356213319	Real period
R	2.7556441616865	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	21424o2 85696p2 24102be2 66950x2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2678h2

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	0	-1	3	-	-3	2	-6	6	-4	2	0	8	6	3	6	8	-13	-12	-7	8	0	6	-10

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Quadratic twists for elliptic curve 2678h2

-4	8	-3	5	13
21424o2	85696p2	24102be2	66950x2	34814v2

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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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