Cremona's table of elliptic curves

6448 = 2⁴ · 13 · 31

Field	Data	Notes
Atkin-Lehner	2- 13+ 31-	Signs for the Atkin-Lehner involutions
Class	6448f	Isogeny class
Conductor	6448	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	4224	Modular degree for the optimal curve
Δ	-104798879744 = -1 · 223 · 13 · 312	Discriminant
Eigenvalues	2-  1 -1 -1 -2 13+  7  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,824,12916]	[a1,a2,a3,a4,a6]
Generators	[30:256:1]	Generators of the group modulo torsion
j	15087533111/25585664	j-invariant
L	4.2079971844841	L(r)(E,1)/r!
Ω	0.72524288026088	Real period
R	0.72527378396504	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	806b1 25792bi1 58032ba1 83824n1	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 6448f1

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	-1	-1	-2	+	7	4	6	-2	-	-7	10	-1	-1	-14	6	-8	8	1	-10	14	-6	-12	4

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Quadratic twists for elliptic curve 6448f1

-4	8	-3	13
806b1	25792bi1	58032ba1	83824n1

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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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