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	5824b	Isogeny class
Conductor	5824	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	2981888 = 215 · 7 · 13	Discriminant
Eigenvalues	2+  0  2 7+  4 13+  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-3884,-93168]	[a1,a2,a3,a4,a6]
Generators	[2703:19495:27]	Generators of the group modulo torsion
j	197747699976/91	j-invariant
L	4.3001496216234	L(r)(E,1)/r!
Ω	0.60475540890363	Real period
R	7.1105600021324	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	5824h4 2912a2 52416br4 40768bf4	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 5824b3

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	2	+	4	+	2	-4	-4	2	0	-2	-2	-4	-8	2	4	-14	-12	8	14	-12	-4	14	-2

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Quadratic twists for elliptic curve 5824b3

-4	8	-3	-7	13
5824h4	2912a2	52416br4	40768bf4	75712ba4

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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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