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	6448k	Isogeny class
Conductor	6448	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	1344	Modular degree for the optimal curve
Δ	-14166256 = -1 · 24 · 134 · 31	Discriminant
Eigenvalues	2- -2  1 -3 -2 13-  6 -3	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-70,267]	[a1,a2,a3,a4,a6]
Generators	[7:13:1]	Generators of the group modulo torsion
j	-2404846336/885391	j-invariant
L	2.5766714508926	L(r)(E,1)/r!
Ω	2.0953204148219	Real period
R	0.3074316740134	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	1612d1 25792y1 58032bj1 83824bd1	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 6448k1

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
-	-2	1	-3	-2	-	6	-3	6	-8	+	-6	11	0	0	12	7	-2	4	3	6	-4	-6	-12	-3

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Quadratic twists for elliptic curve 6448k1

-4	8	-3	13
1612d1	25792y1	58032bj1	83824bd1

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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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