Cremona's table of elliptic curves

576 = 2⁶ · 3²

Field	Data	Notes
Atkin-Lehner	2+ 3+	Signs for the Atkin-Lehner involutions
Class	576a	Isogeny class
Conductor	576	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	-20155392 = -1 · 210 · 39	Discriminant
Eigenvalues	2+ 3+  0 -4  0 -2  0 -8	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,0,-216]	[a1,a2,a3,a4,a6]
Generators	[10:28:1]	Generators of the group modulo torsion
j	0	j-invariant
L	1.9430318018415	L(r)(E,1)/r!
Ω	0.99149247513406	Real period
R	1.9597040326289	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	576e3 36a3 576a1 14400l3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 576a3

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
+	+	0	-4	0	-2	0	-8	0	0	-4	10	0	-8	0	0	0	-14	16	0	-10	-4	0	0	14

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Quadratic twists for elliptic curve 576a3

-4	8	-3	5	-7	-11	13
576e3	36a3	576a1	14400l3	28224i3	69696o3	97344c3

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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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