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	6496f	Isogeny class
Conductor	6496	Conductor
∏ cp	32	Product of Tamagawa factors cp
deg	15360	Modular degree for the optimal curve
Δ	-684766121984 = -1 · 212 · 78 · 29	Discriminant
Eigenvalues	2+ -3 -1 7- -1 -7 -6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,2132,-12224]	[a1,a2,a3,a4,a6]
Generators	[118:-1372:1] [13:133:1]	Generators of the group modulo torsion
j	261652787136/167179229	j-invariant
L	3.4049138629475	L(r)(E,1)/r!
Ω	0.51954814951238	Real period
R	0.20480018707983	Regulator
r	2	Rank of the group of rational points
S	0.99999999999999	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	6496b1 12992bn1 58464be1 45472n1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 6496f1

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
+	-3	-1	-	-1	-7	-6	-4	-6	+	5	-8	0	3	-3	-9	6	2	-12	10	-4	3	-18	-16	-12

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Quadratic twists for elliptic curve 6496f1

-4	8	-3	-7
6496b1	12992bn1	58464be1	45472n1

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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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