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	5712x	Isogeny class
Conductor	5712	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	20160	Modular degree for the optimal curve
Δ	-140694243508224 = -1 · 219 · 33 · 7 · 175	Discriminant
Eigenvalues	2- 3-  3 7- -1  1 17+ -6	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-35264,2600244]	[a1,a2,a3,a4,a6]
j	-1184052061112257/34349180544	j-invariant
L	3.476984177906	L(r)(E,1)/r!
Ω	0.57949736298434	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	714e1 22848cf1 17136bs1 39984cn1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 5712x1

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
-	-	3	-	-1	1	+	-6	2	-2	0	5	4	9	0	11	-4	6	11	12	-5	15	-1	9	-9

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Quadratic twists for elliptic curve 5712x1

-4	8	-3	-7	17
714e1	22848cf1	17136bs1	39984cn1	97104bq1

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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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