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	8710i	Isogeny class
Conductor	8710	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	65280	Modular degree for the optimal curve
Δ	598557613556240 = 24 · 5 · 135 · 674	Discriminant
Eigenvalues	2- -2 5+ -4  2 13+ -6 -2	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-32691,1944145]	[a1,a2,a3,a4,a6]
Generators	[-64:1975:1]	Generators of the group modulo torsion
j	3863751256268453809/598557613556240	j-invariant
L	3.4479814692151	L(r)(E,1)/r!
Ω	0.49354730115144	Real period
R	1.7465304040621	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	69680p1 78390x1 43550h1 113230l1	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 8710i1

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	+	-4	2	+	-6	-2	2	10	10	6	-2	-6	-4	-6	10	2	-	6	-6	-4	0	18	14

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Quadratic twists for elliptic curve 8710i1

-4	-3	5	13
69680p1	78390x1	43550h1	113230l1

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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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