Cremona's table of elliptic curves

9576 = 2³ · 3² · 7 · 19

Field	Data	Notes
Atkin-Lehner	2+ 3+ 7- 19-	Signs for the Atkin-Lehner involutions
Class	9576f	Isogeny class
Conductor	9576	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	3072	Modular degree for the optimal curve
Δ	1091664 = 24 · 33 · 7 · 192	Discriminant
Eigenvalues	2+ 3+ -2 7- -2  2  2 19-	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-2526,48865]	[a1,a2,a3,a4,a6]
Generators	[33:38:1]	Generators of the group modulo torsion
j	4126102419456/2527	j-invariant
L	3.9175000454008	L(r)(E,1)/r!
Ω	2.2736574848051	Real period
R	0.86149740486013	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	19152d1 76608o1 9576s1 67032c1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 9576f1

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
+	+	-2	-	-2	2	2	-	-6	-4	4	2	2	4	8	-8	4	6	-4	10	6	-16	-12	-6	-2

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Quadratic twists for elliptic curve 9576f1

-4	8	-3	-7
19152d1	76608o1	9576s1	67032c1

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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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