Cremona's table of elliptic curves

5408 = 2⁵ · 13²

Field	Data	Notes
Atkin-Lehner	2- 13-	Signs for the Atkin-Lehner involutions
Class	5408k	Isogeny class
Conductor	5408	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	6240	Modular degree for the optimal curve
Δ	678687959872 = 26 · 139	Discriminant
Eigenvalues	2-  0 -4  0  0 13-  2  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-2197,0]	[a1,a2,a3,a4,a6]
Generators	[-9:138:1]	Generators of the group modulo torsion
j	1728	j-invariant
L	2.7445048147261	L(r)(E,1)/r!
Ω	0.76597518762192	Real period
R	3.5830205195638	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	5408k1 10816bl2 48672ba1 5408e1	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 5408k1

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
-	0	-4	0	0	-	2	0	0	10	0	12	-8	0	0	14	0	-10	0	0	-16	0	0	-16	-8

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Quadratic twists for elliptic curve 5408k1

-4	8	-3	13
5408k1	10816bl2	48672ba1	5408e1

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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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