Cremona's table of elliptic curves

8715 = 3 · 5 · 7 · 83

Field	Data	Notes
Atkin-Lehner	3- 5+ 7- 83+	Signs for the Atkin-Lehner involutions
Class	8715j	Isogeny class
Conductor	8715	Conductor
∏ cp	12	Product of Tamagawa factors cp
Δ	68630625 = 33 · 54 · 72 · 83	Discriminant
Eigenvalues	1 3- 5+ 7-  0  2 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-585649,172456991]	[a1,a2,a3,a4,a6]
Generators	[3734:5479:8]	Generators of the group modulo torsion
j	22214414151394614599689/68630625	j-invariant
L	5.9254640698131	L(r)(E,1)/r!
Ω	0.91769216528826	Real period
R	2.1523063666096	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	26145t4 43575b4 61005j4	Quadratic twists by: -3 5 -7

Hecke Eigenvalues for elliptic curve 8715j4

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
1	-	+	-	0	2	-2	-4	0	6	0	-2	2	0	-8	-6	-8	-2	-8	8	-10	8	+	6	-2

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Quadratic twists for elliptic curve 8715j4

-3	5	-7
26145t4	43575b4	61005j4

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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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