Cremona's table of elliptic curves

2624 = 2⁶ · 41

Field	Data	Notes
Atkin-Lehner	2+ 41-	Signs for the Atkin-Lehner involutions
Class	2624c	Isogeny class
Conductor	2624	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	384	Modular degree for the optimal curve
Δ	671744 = 214 · 41	Discriminant
Eigenvalues	2+ -2 -2 -2 -2 -6 -6  2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-49,111]	[a1,a2,a3,a4,a6]
Generators	[-6:15:1] [-5:16:1]	Generators of the group modulo torsion
j	810448/41	j-invariant
L	2.6661046169569	L(r)(E,1)/r!
Ω	2.8337360190372	Real period
R	0.94084438319124	Regulator
r	2	Rank of the group of rational points
S	0.99999999999963	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	2624h1 328b1 23616h1 65600u1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2624c1

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	-2	-2	-6	-6	2	0	-6	-8	-10	-	0	-6	2	4	2	10	-2	-2	-2	-12	10	-6

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Quadratic twists for elliptic curve 2624c1

-4	8	-3	5	-7	41
2624h1	328b1	23616h1	65600u1	128576x1	107584b1

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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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