Cremona's table of elliptic curves

5408 = 2⁵ · 13²

Field	Data	Notes
Atkin-Lehner	2- 13-	Signs for the Atkin-Lehner involutions
Class	5408l	Isogeny class
Conductor	5408	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	22464	Modular degree for the optimal curve
Δ	-5429503678976 = -1 · 29 · 139	Discriminant
Eigenvalues	2-  3 -3  1 -4 13-  5 -6	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-15379,742586]	[a1,a2,a3,a4,a6]
Generators	[5070:57122:27]	Generators of the group modulo torsion
j	-74088	j-invariant
L	5.4289746373386	L(r)(E,1)/r!
Ω	0.76514995139083	Real period
R	3.5476540431521	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	5408g1 10816w1 48672y1 5408f1	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 5408l1

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	-3	1	-4	-	5	-6	-6	-4	0	-3	12	-3	-7	-2	2	-12	-4	11	6	-6	-10	6	0

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Quadratic twists for elliptic curve 5408l1

-4	8	-3	13
5408g1	10816w1	48672y1	5408f1

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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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