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	5712z	Isogeny class
Conductor	5712	Conductor
∏ cp	68	Product of Tamagawa factors cp
deg	39168	Modular degree for the optimal curve
Δ	-21590483079868416 = -1 · 212 · 317 · 74 · 17	Discriminant
Eigenvalues	2- 3-  1 7- -3  3 17- -3	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,57035,-4723549]	[a1,a2,a3,a4,a6]
Generators	[110:1701:1]	Generators of the group modulo torsion
j	5009339741732864/5271114033171	j-invariant
L	5.0462539710934	L(r)(E,1)/r!
Ω	0.20713408139636	Real period
R	0.35826850280595	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	357a1 22848ch1 17136bj1 39984bm1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 5712z1

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	3	-	-3	-7	-6	-10	4	-9	-9	-6	-10	2	0	12	12	6	-10	-10	-4	8

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Quadratic twists for elliptic curve 5712z1

-4	8	-3	-7	17
357a1	22848ch1	17136bj1	39984bm1	97104bf1

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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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