Cremona's table of elliptic curves

5772 = 2² · 3 · 13 · 37

Field	Data	Notes
Atkin-Lehner	2- 3+ 13+ 37+	Signs for the Atkin-Lehner involutions
Class	5772a	Isogeny class
Conductor	5772	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-810777786624 = -1 · 28 · 34 · 134 · 372	Discriminant
Eigenvalues	2- 3+  2  0  0 13+ -6 -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-1652,51000]	[a1,a2,a3,a4,a6]
j	-1948842487888/3167100729	j-invariant
L	1.6019439850215	L(r)(E,1)/r!
Ω	0.80097199251075	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	23088n2 92352bi2 17316a2 75036d2	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 5772a2

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	0	+	-6	-2	-6	10	2	+	-10	10	8	10	14	10	8	8	-10	-6	12	-6	10

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Quadratic twists for elliptic curve 5772a2

-4	8	-3	13
23088n2	92352bi2	17316a2	75036d2

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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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