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	6496c	Isogeny class
Conductor	6496	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	24113152 = 212 · 7 · 292	Discriminant
Eigenvalues	2+  0 -2 7+ -6  2 -4 -8	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-76,-96]	[a1,a2,a3,a4,a6]
Generators	[-6:12:1] [-4:12:1]	Generators of the group modulo torsion
j	11852352/5887	j-invariant
L	4.5604491082062	L(r)(E,1)/r!
Ω	1.7019087782392	Real period
R	1.3398042146904	Regulator
r	2	Rank of the group of rational points
S	0.99999999999985	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	6496k2 12992a1 58464x2 45472q2	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 6496c2

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

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Quadratic twists for elliptic curve 6496c2

-4	8	-3	-7
6496k2	12992a1	58464x2	45472q2

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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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