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	9576j	Isogeny class
Conductor	9576	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-2750364481536 = -1 · 211 · 312 · 7 · 192	Discriminant
Eigenvalues	2+ 3- -2 7+ -6 -2  8 19-	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,1149,-78370]	[a1,a2,a3,a4,a6]
Generators	[38:142:1]	Generators of the group modulo torsion
j	112363774/1842183	j-invariant
L	3.3634228391738	L(r)(E,1)/r!
Ω	0.3939147484673	Real period
R	4.2692268470026	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	19152w2 76608bd2 3192l2 67032x2	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 9576j2

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

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Quadratic twists for elliptic curve 9576j2

-4	8	-3	-7
19152w2	76608bd2	3192l2	67032x2

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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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