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	2	Product of Tamagawa factors cp
deg	864	Modular degree for the optimal curve
Δ	873936 = 24 · 33 · 7 · 172	Discriminant
Eigenvalues	2- 3+  2 7+  0 -2 17+ -6	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-57,180]	[a1,a2,a3,a4,a6]
j	1302642688/54621	j-invariant
L	1.3908023286222	L(r)(E,1)/r!
Ω	2.7816046572445	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	1428d1 22848ck1 17136be1 39984dq1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 5712k1

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 5712k1

-4	8	-3	-7	17
1428d1	22848ck1	17136be1	39984dq1	97104cq1

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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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