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	62496r	Isogeny class
Conductor	62496	Conductor
∏ cp	320	Product of Tamagawa factors cp
Δ	417125712157765632 = 212 · 38 · 75 · 314	Discriminant
Eigenvalues	2+ 3-  0 7- -6 -6  0 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-772140,-259296032]	[a1,a2,a3,a4,a6]
Generators	[-534:868:1] [-478:756:1]	Generators of the group modulo torsion
j	17050000247272000/139694557023	j-invariant
L	9.9108251912665	L(r)(E,1)/r!
Ω	0.16113510050164	Real period
R	0.76882885544692	Regulator
r	2	Rank of the group of rational points
S	0.99999999999862	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	62496be2 124992dc1 20832bg2	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 62496r2

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

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Quadratic twists for elliptic curve 62496r2

-4	8	-3
62496be2	124992dc1	20832bg2

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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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