Cremona's table of elliptic curves

117670 = 2 · 5 · 7 · 41²

Field	Data	Notes
Atkin-Lehner	2- 5+ 7- 41+	Signs for the Atkin-Lehner involutions
Class	117670m	Isogeny class
Conductor	117670	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	570250014132050 = 2 · 52 · 74 · 416	Discriminant
Eigenvalues	2-  0 5+ 7- -4  6 -2  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-449983,-116064619]	[a1,a2,a3,a4,a6]
Generators	[61844:1167599:64]	Generators of the group modulo torsion
j	2121328796049/120050	j-invariant
L	9.2451697546248	L(r)(E,1)/r!
Ω	0.18433256997538	Real period
R	6.2693544358871	Regulator
r	1	Rank of the group of rational points
S	1.0000000035257	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	70a3	Quadratic twists by: 41

Hecke Eigenvalues for elliptic curve 117670m4

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	+	-	-4	6	-2	0	0	-6	8	-10	+	4	-8	2	-8	-14	12	16	2	8	8	-10	-2

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Quadratic twists for elliptic curve 117670m4

41
70a3

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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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