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	6448j	Isogeny class
Conductor	6448	Conductor
∏ cp	12	Product of Tamagawa factors cp
Δ	-4089122572797476864 = -1 · 221 · 133 · 316	Discriminant
Eigenvalues	2- -1  3  1  0 13-  3 -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-410384,140510656]	[a1,a2,a3,a4,a6]
Generators	[8450:774566:1]	Generators of the group modulo torsion
j	-1866105028152018577/998320940624384	j-invariant
L	4.1627073197994	L(r)(E,1)/r!
Ω	0.22959924929695	Real period
R	1.5108598033842	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	806e2 25792v2 58032bl2 83824ba2	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 6448j2

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	3	1	0	-	3	-2	-6	-6	+	-7	-6	1	-3	6	0	-10	4	3	2	-8	0	0	-10

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Quadratic twists for elliptic curve 6448j2

-4	8	-3	13
806e2	25792v2	58032bl2	83824ba2

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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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