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	6461c	Isogeny class
Conductor	6461	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	672	Modular degree for the optimal curve
Δ	-2216123 = -1 · 74 · 13 · 71	Discriminant
Eigenvalues	0 -1 -2 7-  0 13- -4  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,21,-69]	[a1,a2,a3,a4,a6]
Generators	[3:3:1]	Generators of the group modulo torsion
j	976191488/2216123	j-invariant
L	2.1008064145353	L(r)(E,1)/r!
Ω	1.3471286951269	Real period
R	0.38986743102843	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	103376m1 58149h1 45227d1 83993b1	Quadratic twists by: -4 -3 -7 13

Hecke Eigenvalues for elliptic curve 6461c1

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
0	-1	-2	-	0	-	-4	0	-2	9	-11	0	9	9	-9	8	-3	4	13	+	-4	9	-6	10	-2

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Quadratic twists for elliptic curve 6461c1

-4	-3	-7	13
103376m1	58149h1	45227d1	83993b1

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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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