Cremona's table of elliptic curves

6715 = 5 · 17 · 79

Field	Data	Notes
Atkin-Lehner	5+ 17- 79+	Signs for the Atkin-Lehner involutions
Class	6715c	Isogeny class
Conductor	6715	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	9648	Modular degree for the optimal curve
Δ	-238358493875 = -1 · 53 · 176 · 79	Discriminant
Eigenvalues	2 -1 5+ -1 -5  0 17-  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-5156,-142719]	[a1,a2,a3,a4,a6]
j	-15161656961880064/238358493875	j-invariant
L	1.6886122043225	L(r)(E,1)/r!
Ω	0.28143536738708	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	107440s1 60435g1 33575b1 114155j1	Quadratic twists by: -4 -3 5 17

Hecke Eigenvalues for elliptic curve 6715c1

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	+	-1	-5	0	-	4	2	6	-7	-5	2	4	-8	-1	-6	8	-4	12	8	+	6	14	8

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Quadratic twists for elliptic curve 6715c1

-4	-3	5	17
107440s1	60435g1	33575b1	114155j1

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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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