Cremona's table of elliptic curves

6496 = 2⁵ · 7 · 29

Field	Data	Notes
Atkin-Lehner	2+ 7+ 29+	Signs for the Atkin-Lehner involutions
Class	6496a	Isogeny class
Conductor	6496	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	727552 = 29 · 72 · 29	Discriminant
Eigenvalues	2+  0 -4 7+  4 -4  0  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-307,-2070]	[a1,a2,a3,a4,a6]
Generators	[162:33:8]	Generators of the group modulo torsion
j	6249839688/1421	j-invariant
L	2.7371350314801	L(r)(E,1)/r!
Ω	1.1405672213595	Real period
R	4.79960318028	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	6496e2 12992z2 58464ba2 45472b2	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 6496a2

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

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Quadratic twists for elliptic curve 6496a2

-4	8	-3	-7
6496e2	12992z2	58464ba2	45472b2

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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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