Cremona's table of elliptic curves

5746 = 2 · 13² · 17

Field	Data	Notes
Atkin-Lehner	2+ 13+ 17+	Signs for the Atkin-Lehner involutions
Class	5746f	Isogeny class
Conductor	5746	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	217152	Modular degree for the optimal curve
Δ	-10836780327266192 = -1 · 24 · 1310 · 173	Discriminant
Eigenvalues	2+ -3  4 -1 -4 13+ 17+ -6	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-719380,-234720992]	[a1,a2,a3,a4,a6]
Generators	[6843804:480136148:1331]	Generators of the group modulo torsion
j	-298652123601/78608	j-invariant
L	2.0882359523828	L(r)(E,1)/r!
Ω	0.081963988433038	Real period
R	12.738740465813	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	45968n1 51714z1 5746i1 97682i1	Quadratic twists by: -4 -3 13 17

Hecke Eigenvalues for elliptic curve 5746f1

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	4	-1	-4	+	+	-6	-1	2	11	6	-6	10	-4	-9	-8	-2	8	-4	-2	-7	0	15	4

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Quadratic twists for elliptic curve 5746f1

-4	-3	13	17
45968n1	51714z1	5746i1	97682i1

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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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