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	8610s	Isogeny class
Conductor	8610	Conductor
∏ cp	768	Product of Tamagawa factors cp
deg	36864	Modular degree for the optimal curve
Δ	59988418560000 = 216 · 36 · 54 · 72 · 41	Discriminant
Eigenvalues	2- 3- 5- 7+  0 -6 -2  0	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-32645,2236737]	[a1,a2,a3,a4,a6]
Generators	[754:-20537:1]	Generators of the group modulo torsion
j	3847463977937161681/59988418560000	j-invariant
L	7.6366828485222	L(r)(E,1)/r!
Ω	0.62562676151916	Real period
R	0.25430107714365	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	68880bx1 25830h1 43050g1 60270q1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 8610s1

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

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Quadratic twists for elliptic curve 8610s1

-4	-3	5	-7
68880bx1	25830h1	43050g1	60270q1

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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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