Cremona's table of elliptic curves

70688 = 2⁵ · 47²

Field	Data	Notes
Atkin-Lehner	2- 47-	Signs for the Atkin-Lehner involutions
Class	70688c	Isogeny class
Conductor	70688	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	52992	Modular degree for the optimal curve
Δ	689869781056 = 26 · 476	Discriminant
Eigenvalues	2-  0  2  0  0 -6  2  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-2209,0]	[a1,a2,a3,a4,a6]
Generators	[-410567038488:-7010818201135:55568042496]	Generators of the group modulo torsion
j	1728	j-invariant
L	6.3343905999312	L(r)(E,1)/r!
Ω	0.76493280572762	Real period
R	16.561953031814	Regulator
r	1	Rank of the group of rational points
S	0.99999999991377	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	70688c1 32a2	Quadratic twists by: -4 -47

Hecke Eigenvalues for elliptic curve 70688c1

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	2	0	0	-6	2	0	0	10	0	-2	-10	0	-	14	0	-10	0	0	6	0	0	10	18

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Quadratic twists for elliptic curve 70688c1

-4	-47
70688c1	32a2

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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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