Cremona's table of elliptic curves

572 = 2² · 11 · 13

Field	Data	Notes
Atkin-Lehner	2- 11- 13-	Signs for the Atkin-Lehner involutions
Class	572a	Isogeny class
Conductor	572	Conductor
∏ cp	18	Product of Tamagawa factors cp
deg	120	Modular degree for the optimal curve
Δ	-57584384 = -1 · 28 · 113 · 132	Discriminant
Eigenvalues	2-  1  3  2 11- 13-  0  2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,91,-121]	[a1,a2,a3,a4,a6]
j	321978368/224939	j-invariant
L	2.2372155071704	L(r)(E,1)/r!
Ω	1.1186077535852	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	2288f1 9152c1 5148d1 14300f1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 572a1

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
-	1	3	2	-	-	0	2	-3	-6	-1	-7	6	8	12	-6	9	2	-7	-3	8	-4	-12	-15	-13

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Quadratic twists for elliptic curve 572a1

-4	8	-3	5	-7	-11	13
2288f1	9152c1	5148d1	14300f1	28028i1	6292d1	7436a1

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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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