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	5772d	Isogeny class
Conductor	5772	Conductor
∏ cp	60	Product of Tamagawa factors cp
deg	10560	Modular degree for the optimal curve
Δ	5907734352 = 24 · 310 · 132 · 37	Discriminant
Eigenvalues	2- 3- -4 -4 -4 13- -8 -6	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-2165,37884]	[a1,a2,a3,a4,a6]
Generators	[-53:81:1] [-21:273:1]	Generators of the group modulo torsion
j	70174287855616/369233397	j-invariant
L	4.5468991512528	L(r)(E,1)/r!
Ω	1.3539197803873	Real period
R	0.22388816122975	Regulator
r	2	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	23088m1 92352f1 17316d1 75036h1	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 5772d1

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	-4	-4	-	-8	-6	-4	0	-6	+	-10	-6	8	-6	12	-6	4	-16	2	14	-4	0	-2

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Quadratic twists for elliptic curve 5772d1

-4	8	-3	13
23088m1	92352f1	17316d1	75036h1

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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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