Cremona's table of elliptic curves

5408 = 2⁵ · 13²

Field	Data	Notes
Atkin-Lehner	2+ 13+	Signs for the Atkin-Lehner involutions
Class	5408c	Isogeny class
Conductor	5408	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	17472	Modular degree for the optimal curve
Δ	-564668382613504 = -1 · 212 · 1310	Discriminant
Eigenvalues	2+  2 -1  0 -4 13+  3  2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-38081,-3067663]	[a1,a2,a3,a4,a6]
Generators	[11127:192932:27]	Generators of the group modulo torsion
j	-10816	j-invariant
L	4.9294838010894	L(r)(E,1)/r!
Ω	0.16998558661783	Real period
R	7.2498555600658	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	5408j1 10816n1 48672bo1 5408i1	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 5408c1

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	0	-4	+	3	2	2	5	-2	-5	-3	-4	-6	13	-12	-7	14	-6	-7	8	-4	-14	2

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Quadratic twists for elliptic curve 5408c1

-4	8	-3	13
5408j1	10816n1	48672bo1	5408i1

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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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