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	24	Product of Tamagawa factors cp
Δ	8705636352 = 211 · 36 · 73 · 17	Discriminant
Eigenvalues	2+ 3+ -2 7-  0  2 17-  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-181367424,-940067661600]	[a1,a2,a3,a4,a6]
Generators	[2735204:533035979:64]	Generators of the group modulo torsion
j	322159999717985454060440834/4250799	j-invariant
L	3.037406583568	L(r)(E,1)/r!
Ω	0.041139568604914	Real period
R	12.305292635815	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	2856h4 22848cw4 17136j4 39984o4	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 5712g3

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 5712g3

-4	8	-3	-7	17
2856h4	22848cw4	17136j4	39984o4	97104r4

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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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