Cremona's table of elliptic curves

7585 = 5 · 37 · 41

Field	Data	Notes
Atkin-Lehner	5+ 37+ 41-	Signs for the Atkin-Lehner involutions
Class	7585a	Isogeny class
Conductor	7585	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-1969040400625 = -1 · 54 · 374 · 412	Discriminant
Eigenvalues	-1  2 5+  2 -6 -6  2 -6	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,2164,-54386]	[a1,a2,a3,a4,a6]
j	1120683397845311/1969040400625	j-invariant
L	0.87115674553485	L(r)(E,1)/r!
Ω	0.43557837276743	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	121360q2 68265j2 37925e2	Quadratic twists by: -4 -3 5

Hecke Eigenvalues for elliptic curve 7585a2

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	2	+	2	-6	-6	2	-6	4	-6	4	+	-	-4	6	2	8	-2	14	-14	14	6	-12	18	2

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Quadratic twists for elliptic curve 7585a2

-4	-3	5
121360q2	68265j2	37925e2

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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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