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	9568k	Isogeny class
Conductor	9568	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	10368	Modular degree for the optimal curve
Δ	-595053056 = -1 · 29 · 133 · 232	Discriminant
Eigenvalues	2-  1 -3 -5  2 13-  3  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-9872,374264]	[a1,a2,a3,a4,a6]
Generators	[98:598:1]	Generators of the group modulo torsion
j	-207832366624904/1162213	j-invariant
L	3.373535365426	L(r)(E,1)/r!
Ω	1.4484786122289	Real period
R	0.19408498319919	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	9568h1 19136c1 86112q1 124384c1	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 9568k1

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	-5	2	-	3	4	+	0	0	-3	6	5	9	-2	-4	0	2	7	8	-4	-6	-10	4

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Quadratic twists for elliptic curve 9568k1

-4	8	-3	13
9568h1	19136c1	86112q1	124384c1

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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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