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	8610k	Isogeny class
Conductor	8610	Conductor
∏ cp	10	Product of Tamagawa factors cp
deg	23520	Modular degree for the optimal curve
Δ	-313834500000 = -1 · 25 · 37 · 56 · 7 · 41	Discriminant
Eigenvalues	2- 3+ 5+ 7+ -1  0  4 -5	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-34451,-2475727]	[a1,a2,a3,a4,a6]
Generators	[221:764:1]	Generators of the group modulo torsion
j	-4521994166332118449/313834500000	j-invariant
L	4.9517148509228	L(r)(E,1)/r!
Ω	0.17521336356684	Real period
R	2.8261056977163	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	68880ck1 25830p1 43050u1 60270br1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 8610k1

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	0	4	-5	3	-8	1	4	-	3	7	-10	5	-1	0	-10	-2	-13	-4	16	-7

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Quadratic twists for elliptic curve 8610k1

-4	-3	5	-7
68880ck1	25830p1	43050u1	60270br1

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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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