Cremona's table of elliptic curves

8610 = 2 · 3 · 5 · 7 · 41

Field	Data	Notes
Atkin-Lehner	2- 3+ 5+ 7+ 41-	Signs for the Atkin-Lehner involutions
Class	8610j	Isogeny class
Conductor	8610	Conductor
∏ cp	160	Product of Tamagawa factors cp
Δ	48849495559200 = 25 · 32 · 52 · 74 · 414	Discriminant
Eigenvalues	2- 3+ 5+ 7+  0 -2  2  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-40116,-3090987]	[a1,a2,a3,a4,a6]
Generators	[-113:179:1]	Generators of the group modulo torsion
j	7139655496778995009/48849495559200	j-invariant
L	4.9875463531834	L(r)(E,1)/r!
Ω	0.33748086713339	Real period
R	0.36946882319199	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	68880cj3 25830o3 43050t3 60270bq3	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 8610j3

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

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Quadratic twists for elliptic curve 8610j3

-4	-3	5	-7
68880cj3	25830o3	43050t3	60270bq3

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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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