Cremona's table of elliptic curves

62496 = 2⁵ · 3² · 7 · 31

Field	Data	Notes
Atkin-Lehner	2- 3- 7- 31-	Signs for the Atkin-Lehner involutions
Class	62496bz	Isogeny class
Conductor	62496	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	2510839296 = 29 · 36 · 7 · 312	Discriminant
Eigenvalues	2- 3-  2 7- -4 -2  0  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-579,-4790]	[a1,a2,a3,a4,a6]
Generators	[4530:58040:27]	Generators of the group modulo torsion
j	57512456/6727	j-invariant
L	7.2550823064468	L(r)(E,1)/r!
Ω	0.98069155865654	Real period
R	7.397924701614	Regulator
r	1	Rank of the group of rational points
S	0.99999999999963	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	62496i2 124992dg2 6944d2	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 62496bz2

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

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Quadratic twists for elliptic curve 62496bz2

-4	8	-3
62496i2	124992dg2	6944d2

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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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