Cremona's table of elliptic curves

5712 = 2⁴ · 3 · 7 · 17

Field	Data	Notes
Atkin-Lehner	2+ 3+ 7- 17-	Signs for the Atkin-Lehner involutions
Class	5712g	Isogeny class
Conductor	5712	Conductor
∏ cp	192	Product of Tamagawa factors cp
Δ	1.7259557071287E+21	Discriminant
Eigenvalues	2+ 3+ -2 7-  0  2 17-  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-11364624,-14606337312]	[a1,a2,a3,a4,a6]
Generators	[-1998:10962:1]	Generators of the group modulo torsion
j	79260902459030376659234/842751810121431609	j-invariant
L	3.037406583568	L(r)(E,1)/r!
Ω	0.082279137209828	Real period
R	3.0763231589538	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	2856h3 22848cw3 17136j3 39984o3	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 5712g4

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

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Quadratic twists for elliptic curve 5712g4

-4	8	-3	-7	17
2856h3	22848cw3	17136j3	39984o3	97104r3

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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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