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	8610r	Isogeny class
Conductor	8610	Conductor
∏ cp	224	Product of Tamagawa factors cp
Δ	94591806491996100 = 22 · 314 · 52 · 76 · 412	Discriminant
Eigenvalues	2- 3- 5- 7+  4 -6 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-2500505,1521632277]	[a1,a2,a3,a4,a6]
j	1729047422759633803829521/94591806491996100	j-invariant
L	4.4731174673915	L(r)(E,1)/r!
Ω	0.31950839052797	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	68880bu2 25830k2 43050f2 60270u2	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 8610r2

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

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Quadratic twists for elliptic curve 8610r2

-4	-3	5	-7
68880bu2	25830k2	43050f2	60270u2

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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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