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	8610o	Isogeny class
Conductor	8610	Conductor
∏ cp	128	Product of Tamagawa factors cp
deg	6144	Modular degree for the optimal curve
Δ	2892960000 = 28 · 32 · 54 · 72 · 41	Discriminant
Eigenvalues	2- 3+ 5- 7-  0 -6 -2  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-510,3387]	[a1,a2,a3,a4,a6]
Generators	[-23:71:1]	Generators of the group modulo torsion
j	14671937276641/2892960000	j-invariant
L	5.8513755930938	L(r)(E,1)/r!
Ω	1.3553705461656	Real period
R	0.53964722134912	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	68880cq1 25830l1 43050o1 60270bg1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 8610o1

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	6	-8	-2	-	4	8	-14	-12	-2	4	-12	2	4	-12	-6	14

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Quadratic twists for elliptic curve 8610o1

-4	-3	5	-7
68880cq1	25830l1	43050o1	60270bg1

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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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