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	9576w	Isogeny class
Conductor	9576	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	-2042966209536 = -1 · 210 · 37 · 7 · 194	Discriminant
Eigenvalues	2- 3- -2 7+ -4 -6 -6 19-	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,2949,-30490]	[a1,a2,a3,a4,a6]
Generators	[19:180:1] [35:340:1]	Generators of the group modulo torsion
j	3799448348/2736741	j-invariant
L	5.2129586346694	L(r)(E,1)/r!
Ω	0.46523730339521	Real period
R	5.6024727559732	Regulator
r	2	Rank of the group of rational points
S	1.0000000000002	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	19152v4 76608bc3 3192a4 67032ce3	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 9576w4

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	+	-4	-6	-6	-	-8	6	0	-2	-6	-4	-4	-2	-12	-10	8	0	10	-12	-16	-6	-10

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Quadratic twists for elliptic curve 9576w4

-4	8	-3	-7
19152v4	76608bc3	3192a4	67032ce3

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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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