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	5712k	Isogeny class
Conductor	5712	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	-155457792 = -1 · 28 · 36 · 72 · 17	Discriminant
Eigenvalues	2- 3+  2 7+  0 -2 17+ -6	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,28,588]	[a1,a2,a3,a4,a6]
j	9148592/607257	j-invariant
L	1.3908023286222	L(r)(E,1)/r!
Ω	1.3908023286222	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	1428d2 22848ck2 17136be2 39984dq2	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 5712k2

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	+	-6	-8	-4	0	10	10	8	8	6	4	-8	4	8	4	0	0	10	0

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Quadratic twists for elliptic curve 5712k2

-4	8	-3	-7	17
1428d2	22848ck2	17136be2	39984dq2	97104cq2

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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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