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	8710a	Isogeny class
Conductor	8710	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	2304	Modular degree for the optimal curve
Δ	29178500 = 22 · 53 · 13 · 672	Discriminant
Eigenvalues	2+  2 5+  0 -2 13+ -2  8	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-78,32]	[a1,a2,a3,a4,a6]
Generators	[-1:11:1]	Generators of the group modulo torsion
j	53540005609/29178500	j-invariant
L	4.1030896986641	L(r)(E,1)/r!
Ω	1.8263261694489	Real period
R	2.2466357692845	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	69680r1 78390bu1 43550x1 113230x1	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 8710a1

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	8	-6	6	4	-2	4	-2	-4	-2	-4	14	+	2	-14	0	-4	-6	-6

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Quadratic twists for elliptic curve 8710a1

-4	-3	5	13
69680r1	78390bu1	43550x1	113230x1

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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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