Cremona's table of elliptic curves

7565 = 5 · 17 · 89

Field	Data	Notes
Atkin-Lehner	5+ 17- 89+	Signs for the Atkin-Lehner involutions
Class	7565a	Isogeny class
Conductor	7565	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	718137965438645 = 5 · 172 · 896	Discriminant
Eigenvalues	1  2 5+ -2 -4 -4 17-  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-22393,-45372]	[a1,a2,a3,a4,a6]
j	1241912091608857369/718137965438645	j-invariant
L	1.7085239820749	L(r)(E,1)/r!
Ω	0.42713099551874	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	4	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	121040p2 68085k2 37825c2 128605a2	Quadratic twists by: -4 -3 5 17

Hecke Eigenvalues for elliptic curve 7565a2

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	-4	-4	-	0	-6	6	8	8	10	10	0	-10	-4	-2	-16	-8	10	16	-14	+	14

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Quadratic twists for elliptic curve 7565a2

-4	-3	5	17
121040p2	68085k2	37825c2	128605a2

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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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