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	20	Product of Tamagawa factors cp
Δ	23537587500000 = 25 · 38 · 58 · 7 · 41	Discriminant
Eigenvalues	2- 3+ 5+ 7+  0 -2  2  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-50036,4280789]	[a1,a2,a3,a4,a6]
Generators	[153:409:1]	Generators of the group modulo torsion
j	13853898649143943489/23537587500000	j-invariant
L	4.9875463531834	L(r)(E,1)/r!
Ω	0.67496173426678	Real period
R	1.477875292768	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	68880cj4 25830o4 43050t4 60270bq4	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 8610j4

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 8610j4

-4	-3	5	-7
68880cj4	25830o4	43050t4	60270bq4

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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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