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	32	Product of Tamagawa factors cp
deg	92160	Modular degree for the optimal curve
Δ	227198753436598272 = 236 · 34 · 74 · 17	Discriminant
Eigenvalues	2- 3- -2 7+ -4 -2 17- -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-1123904,-458409420]	[a1,a2,a3,a4,a6]
j	38331145780597164097/55468445663232	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	2	Number of elements in the torsion subgroup
Twists	714g1 22848bx1 17136y1 39984bv1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 5712t1

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 5712t1

-4	8	-3	-7	17
714g1	22848bx1	17136y1	39984bv1	97104cb1

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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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