Cremona's table of elliptic curves

7592 = 2³ · 13 · 73

Field	Data	Notes
Atkin-Lehner	2+ 13- 73-	Signs for the Atkin-Lehner involutions
Class	7592b	Isogeny class
Conductor	7592	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	1664	Modular degree for the optimal curve
Δ	-141879296 = -1 · 211 · 13 · 732	Discriminant
Eigenvalues	2+ -1 -3  1  0 13-  3  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-72,-596]	[a1,a2,a3,a4,a6]
Generators	[45:292:1]	Generators of the group modulo torsion
j	-20436626/69277	j-invariant
L	2.6819414403199	L(r)(E,1)/r!
Ω	0.75258334313535	Real period
R	1.7818235447164	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	15184c1 60736b1 68328j1 98696d1	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 7592b1

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
+	-1	-3	1	0	-	3	0	-2	-8	-4	7	10	-9	13	-2	4	2	4	1	-	2	-6	2	10

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Quadratic twists for elliptic curve 7592b1

-4	8	-3	13
15184c1	60736b1	68328j1	98696d1

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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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