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	7579b	Isogeny class
Conductor	7579	Conductor
∏ cp	24	Product of Tamagawa factors cp
deg	49920	Modular degree for the optimal curve
Δ	-6963399500259059 = -1 · 11 · 134 · 536	Discriminant
Eigenvalues	0  1  3  2 11+ 13-  0 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-394919,95476300]	[a1,a2,a3,a4,a6]
Generators	[-46300:112275:64]	Generators of the group modulo torsion
j	-6811596250443151409152/6963399500259059	j-invariant
L	5.0518475637773	L(r)(E,1)/r!
Ω	0.41808386642106	Real period
R	4.5312507574941	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	121264q1 68211e1 83369c1 98527k1	Quadratic twists by: -4 -3 -11 13

Hecke Eigenvalues for elliptic curve 7579b1

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	1	3	2	+	-	0	-4	-3	0	-7	-1	0	-4	0	-	9	-10	-13	15	2	-10	-6	-9	-19

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Quadratic twists for elliptic curve 7579b1

-4	-3	-11	13
121264q1	68211e1	83369c1	98527k1

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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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