Cremona's table of elliptic curves

2624 = 2⁶ · 41

Field	Data	Notes
Atkin-Lehner	2+ 41+	Signs for the Atkin-Lehner involutions
Class	2624b	Isogeny class
Conductor	2624	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	881328128 = 219 · 412	Discriminant
Eigenvalues	2+  2  2 -4  2 -4 -2 -6	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-737,-7327]	[a1,a2,a3,a4,a6]
Generators	[-384:235:27]	Generators of the group modulo torsion
j	169112377/3362	j-invariant
L	4.3275147762562	L(r)(E,1)/r!
Ω	0.91729339514753	Real period
R	4.717699701261	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	2624g2 82a2 23616u2 65600m2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2624b2

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	-4	2	-4	-2	-6	-8	0	-8	-2	+	12	4	4	-8	14	2	8	10	4	-12	-14	6

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Quadratic twists for elliptic curve 2624b2

-4	8	-3	5	-7	41
2624g2	82a2	23616u2	65600m2	128576br2	107584d2

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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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