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	6448i	Isogeny class
Conductor	6448	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	-8.7287134050307E+19	Discriminant
Eigenvalues	2-  1  1 -3 -2 13-  3  0	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,1070160,-142767148]	[a1,a2,a3,a4,a6]
Generators	[15649549835:-745560350342:48627125]	Generators of the group modulo torsion
j	33090970201326732239/21310335461500826	j-invariant
L	4.5054465505275	L(r)(E,1)/r!
Ω	0.10952043792582	Real period
R	10.284488073311	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	806f2 25792w2 58032bi2 83824x2	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 6448i2

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	-3	-2	-	3	0	6	10	+	3	2	-9	-3	-6	10	-8	-8	3	-6	-10	6	0	-12

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Quadratic twists for elliptic curve 6448i2

-4	8	-3	13
806f2	25792w2	58032bi2	83824x2

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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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