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	9576k	Isogeny class
Conductor	9576	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	-513829293493807872 = -1 · 28 · 39 · 710 · 192	Discriminant
Eigenvalues	2+ 3-  4 7+  0 -2 -4 19-	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-956703,361822610]	[a1,a2,a3,a4,a6]
Generators	[295:10260:1]	Generators of the group modulo torsion
j	-518904725785387216/2753286252003	j-invariant
L	5.4844069434951	L(r)(E,1)/r!
Ω	0.2951113102783	Real period
R	2.3230247166413	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	19152y2 76608bn2 3192m2 67032bb2	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 9576k2

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
+	-	4	+	0	-2	-4	-	-4	-4	0	-10	-10	4	6	0	-4	-10	-4	2	-2	4	14	6	-18

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Quadratic twists for elliptic curve 9576k2

-4	8	-3	-7
19152y2	76608bn2	3192m2	67032bb2

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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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