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	8610p	Isogeny class
Conductor	8610	Conductor
∏ cp	1890	Product of Tamagawa factors cp
deg	151200	Modular degree for the optimal curve
Δ	-1639741740495667200 = -1 · 221 · 33 · 52 · 75 · 413	Discriminant
Eigenvalues	2- 3- 5+ 7- -3 -4  0 -7	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,132084,58784400]	[a1,a2,a3,a4,a6]
Generators	[-222:4416:1]	Generators of the group modulo torsion
j	254843842209078249791/1639741740495667200	j-invariant
L	7.0728995411932	L(r)(E,1)/r!
Ω	0.1932757081566	Real period
R	0.17426128884439	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	68880bh1 25830r1 43050b1 60270z1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 8610p1

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
-	-	+	-	-3	-4	0	-7	3	0	5	8	-	-1	-3	-6	-3	-13	-4	-6	2	5	-12	-12	-1

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Quadratic twists for elliptic curve 8610p1

-4	-3	5	-7
68880bh1	25830r1	43050b1	60270z1

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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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