Cremona's table of elliptic curves

8710 = 2 · 5 · 13 · 67

Field	Data	Notes
Atkin-Lehner	2- 5- 13- 67+	Signs for the Atkin-Lehner involutions
Class	8710m	Isogeny class
Conductor	8710	Conductor
∏ cp	588	Product of Tamagawa factors cp
deg	846720	Modular degree for the optimal curve
Δ	576876734081024000 = 214 · 53 · 137 · 672	Discriminant
Eigenvalues	2-  2 5-  0  2 13- -2  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-163410455,-804089976275]	[a1,a2,a3,a4,a6]
j	482573233994539531386378766321/576876734081024000	j-invariant
L	6.2072170192685	L(r)(E,1)/r!
Ω	0.042225966117473	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	69680bl1 78390k1 43550e1 113230e1	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 8710m1

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

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Quadratic twists for elliptic curve 8710m1

-4	-3	5	13
69680bl1	78390k1	43550e1	113230e1

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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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