Cremona's table of elliptic curves

6958 = 2 · 7² · 71

Field	Data	Notes
Atkin-Lehner	2+ 7- 71-	Signs for the Atkin-Lehner involutions
Class	6958h	Isogeny class
Conductor	6958	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	9438152281766684 = 22 · 716 · 71	Discriminant
Eigenvalues	2+  2 -2 7-  4  0  4 -6	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-57061,2358945]	[a1,a2,a3,a4,a6]
Generators	[-1674:19065:8]	Generators of the group modulo torsion
j	174648757219273/80222970716	j-invariant
L	3.8963250976856	L(r)(E,1)/r!
Ω	0.36680079892162	Real period
R	5.311227659728	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	55664q2 62622cb2 994b2	Quadratic twists by: -4 -3 -7

Hecke Eigenvalues for elliptic curve 6958h2

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	-2	-	4	0	4	-6	0	-2	0	-2	0	-4	-4	6	-8	-8	12	-	-2	4	-6	-14	8

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Quadratic twists for elliptic curve 6958h2

-4	-3	-7
55664q2	62622cb2	994b2

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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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