Cremona's table of elliptic curves

70688 = 2⁵ · 47²

Field	Data	Notes
Atkin-Lehner	2- 47-	Signs for the Atkin-Lehner involutions
Class	70688f	Isogeny class
Conductor	70688	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	379008	Modular degree for the optimal curve
Δ	-12191378770821632 = -1 · 29 · 478	Discriminant
Eigenvalues	2-  1  2 -2  4  4 -3  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,34608,4710488]	[a1,a2,a3,a4,a6]
Generators	[2647271566:96288306382:2048383]	Generators of the group modulo torsion
j	376	j-invariant
L	9.1324884800544	L(r)(E,1)/r!
Ω	0.28096810349356	Real period
R	16.251824258801	Regulator
r	1	Rank of the group of rational points
S	0.99999999993899	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	70688a1 70688g1	Quadratic twists by: -4 -47

Hecke Eigenvalues for elliptic curve 70688f1

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
-	1	2	-2	4	4	-3	4	8	-8	0	2	-11	-1	-	-6	-9	8	5	12	-1	10	-16	7	18

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Quadratic twists for elliptic curve 70688f1

-4	-47
70688a1	70688g1

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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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