Cremona's table of elliptic curves

6461 = 7 · 13 · 71

Field	Data	Notes
Atkin-Lehner	7+ 13- 71-	Signs for the Atkin-Lehner involutions
Class	6461b	Isogeny class
Conductor	6461	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	4312	Modular degree for the optimal curve
Δ	-760130189 = -1 · 77 · 13 · 71	Discriminant
Eigenvalues	1  0  3 7+  0 13- -3  6	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-5143,143262]	[a1,a2,a3,a4,a6]
Generators	[22:190:1]	Generators of the group modulo torsion
j	-15045990520540617/760130189	j-invariant
L	5.3776187316004	L(r)(E,1)/r!
Ω	1.5074519577389	Real period
R	3.5673566271834	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	103376r1 58149f1 45227i1 83993e1	Quadratic twists by: -4 -3 -7 13

Hecke Eigenvalues for elliptic curve 6461b1

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	3	+	0	-	-3	6	-3	-3	7	0	-2	6	-7	-8	-3	-2	-14	-	-11	0	-6	15	-8

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Quadratic twists for elliptic curve 6461b1

-4	-3	-7	13
103376r1	58149f1	45227i1	83993e1

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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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