Cremona's table of elliptic curves

6413 = 11² · 53

Field	Data	Notes
Atkin-Lehner	11+ 53+	Signs for the Atkin-Lehner involutions
Class	6413b	Isogeny class
Conductor	6413	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	6864	Modular degree for the optimal curve
Δ	-124971227623 = -1 · 119 · 53	Discriminant
Eigenvalues	-1 -2 -2  4 11+  0  4 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,1026,-11285]	[a1,a2,a3,a4,a6]
Generators	[417:2252:27]	Generators of the group modulo torsion
j	50653/53	j-invariant
L	1.6690827738687	L(r)(E,1)/r!
Ω	0.56609966884431	Real period
R	5.8967806049989	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	102608g1 57717o1 6413a1	Quadratic twists by: -4 -3 -11

Hecke Eigenvalues for elliptic curve 6413b1

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	-2	-2	4	+	0	4	-4	2	0	10	-10	-6	-8	-4	+	12	-10	-6	-14	14	8	12	-6	2

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Quadratic twists for elliptic curve 6413b1

-4	-3	-11
102608g1	57717o1	6413a1

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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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