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	8710h	Isogeny class
Conductor	8710	Conductor
∏ cp	54	Product of Tamagawa factors cp
Δ	5286210488000 = 26 · 53 · 133 · 673	Discriminant
Eigenvalues	2+ -2 5- -1 -6 13-  0 -7	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-13403,-587994]	[a1,a2,a3,a4,a6]
Generators	[-73:88:1] [-68:134:1]	Generators of the group modulo torsion
j	266246057186165161/5286210488000	j-invariant
L	3.3344927153132	L(r)(E,1)/r!
Ω	0.44424947635019	Real period
R	1.250983547468	Regulator
r	2	Rank of the group of rational points
S	1.0000000000003	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	69680be2 78390bs2 43550p2 113230q2	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 8710h2

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	-	-1	-6	-	0	-7	-9	3	-4	-7	-3	-10	6	-9	-9	8	-	-3	-7	-1	0	6	-10

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Quadratic twists for elliptic curve 8710h2

-4	-3	5	13
69680be2	78390bs2	43550p2	113230q2

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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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