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	5712t	Isogeny class
Conductor	5712	Conductor
∏ cp	512	Product of Tamagawa factors cp
Δ	2.2629129252564E+21	Discriminant
Eigenvalues	2- 3- -2 7+ -4 -2 17- -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-13744704,19474747956]	[a1,a2,a3,a4,a6]
j	70108386184777836280897/552468975892674624	j-invariant
L	1.1731267761782	L(r)(E,1)/r!
Ω	0.14664084702228	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	8	Number of elements in the torsion subgroup
Twists	714g3 22848bx4 17136y3 39984bv4	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 5712t3

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

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Quadratic twists for elliptic curve 5712t3

-4	8	-3	-7	17
714g3	22848bx4	17136y3	39984bv4	97104cb4

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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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