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	8610i	Isogeny class
Conductor	8610	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	-2.2625145296437E+23	Discriminant
Eigenvalues	2- 3+ 5+ 7+ -6  0 -8 -6	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-44050241,-114852413041]	[a1,a2,a3,a4,a6]
j	-9452976518979190126790533009/226251452964372088050000	j-invariant
L	0.93630648089715	L(r)(E,1)/r!
Ω	0.029259577528036	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	4	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	68880ci2 25830q2 43050s2 60270bu2	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 8610i2

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
-	+	+	+	-6	0	-8	-6	0	-2	4	2	+	4	-4	0	0	2	8	-2	-6	10	-4	-2	8

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Quadratic twists for elliptic curve 8610i2

-4	-3	5	-7
68880ci2	25830q2	43050s2	60270bu2

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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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