Cremona's table of elliptic curves

9568 = 2⁵ · 13 · 23

Field	Data	Notes
Atkin-Lehner	2- 13- 23+	Signs for the Atkin-Lehner involutions
Class	9568j	Isogeny class
Conductor	9568	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	3456	Modular degree for the optimal curve
Δ	-206974976 = -1 · 212 · 133 · 23	Discriminant
Eigenvalues	2-  1 -3  4 -1 13-  0  7	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-317,-2389]	[a1,a2,a3,a4,a6]
Generators	[53:364:1]	Generators of the group modulo torsion
j	-862801408/50531	j-invariant
L	4.7507986188238	L(r)(E,1)/r!
Ω	0.56366121778764	Real period
R	1.4047440994996	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	9568g1 19136b1 86112p1 124384b1	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 9568j1

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	4	-1	-	0	7	+	-6	-6	6	-6	-4	-6	4	2	6	-1	-14	-4	14	-9	2	7

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Quadratic twists for elliptic curve 9568j1

-4	8	-3	13
9568g1	19136b1	86112p1	124384b1

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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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