Cremona's table of elliptic curves

7579 = 11 · 13 · 53

Field	Data	Notes
Atkin-Lehner	11- 13+ 53+	Signs for the Atkin-Lehner involutions
Class	7579d	Isogeny class
Conductor	7579	Conductor
∏ cp	20	Product of Tamagawa factors cp
deg	11040	Modular degree for the optimal curve
Δ	-76454291771 = -1 · 115 · 132 · 532	Discriminant
Eigenvalues	0 -3 -3 -4 11- 13+ -2  2	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,776,10380]	[a1,a2,a3,a4,a6]
Generators	[6:123:1] [36:291:1]	Generators of the group modulo torsion
j	51678378196992/76454291771	j-invariant
L	2.3662517120466	L(r)(E,1)/r!
Ω	0.73827049329344	Real period
R	0.16025641912692	Regulator
r	2	Rank of the group of rational points
S	1.0000000000005	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	121264f1 68211a1 83369e1 98527c1	Quadratic twists by: -4 -3 -11 13

Hecke Eigenvalues for elliptic curve 7579d1

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	-3	-3	-4	-	+	-2	2	1	4	-9	-3	0	0	0	+	-9	-2	9	9	-2	-4	-16	-7	-5

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Quadratic twists for elliptic curve 7579d1

-4	-3	-11	13
121264f1	68211a1	83369e1	98527c1

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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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