Cremona's table of elliptic curves

5824 = 2⁶ · 7 · 13

Field	Data	Notes
Atkin-Lehner	2- 7+ 13-	Signs for the Atkin-Lehner involutions
Class	5824x	Isogeny class
Conductor	5824	Conductor
∏ cp	20	Product of Tamagawa factors cp
deg	26880	Modular degree for the optimal curve
Δ	-87209680044032 = -1 · 225 · 7 · 135	Discriminant
Eigenvalues	2-  3  0 7+ -5 13- -4  2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-1420,-449776]	[a1,a2,a3,a4,a6]
Generators	[3990:43264:27]	Generators of the group modulo torsion
j	-1207949625/332678528	j-invariant
L	6.1176432487386	L(r)(E,1)/r!
Ω	0.27061788260348	Real period
R	1.1303102348381	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	5824o1 1456f1 52416fc1 40768de1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 5824x1

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	0	+	-5	-	-4	2	-5	-4	-1	-7	-9	-12	7	4	-6	-13	11	0	7	17	4	14	5

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Quadratic twists for elliptic curve 5824x1

-4	8	-3	-7	13
5824o1	1456f1	52416fc1	40768de1	75712dd1

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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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