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	8	Product of Tamagawa factors cp
Δ	6551207936 = 215 · 7 · 134	Discriminant
Eigenvalues	2+  0  2 7+  4 13+  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-524,2480]	[a1,a2,a3,a4,a6]
Generators	[22:40:1]	Generators of the group modulo torsion
j	485587656/199927	j-invariant
L	4.3001496216234	L(r)(E,1)/r!
Ω	1.2095108178073	Real period
R	1.7776400005331	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	5824h3 2912a3 52416br3 40768bf3	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 5824b4

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 5824b4

-4	8	-3	-7	13
5824h3	2912a3	52416br3	40768bf3	75712ba3

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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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