Cremona's table of elliptic curves

576 = 2⁶ · 3²

Field	Data	Notes
Atkin-Lehner	2- 3-	Signs for the Atkin-Lehner involutions
Class	576i	Isogeny class
Conductor	576	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	143327232 = 216 · 37	Discriminant
Eigenvalues	2- 3- -2  0 -4  2 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-2316,42896]	[a1,a2,a3,a4,a6]
Generators	[10:144:1]	Generators of the group modulo torsion
j	28756228/3	j-invariant
L	1.9003720950219	L(r)(E,1)/r!
Ω	1.7607876529006	Real period
R	0.53963693233859	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	576d3 144b4 192d3 14400ds4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 576i4

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	0	-4	2	-2	-4	-8	6	-8	-6	6	4	0	-2	-4	2	-4	8	10	8	4	6	2

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Quadratic twists for elliptic curve 576i4

-4	8	-3	5	-7	-11	13
576d3	144b4	192d3	14400ds4	28224fv4	69696gl4	97344fb4

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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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