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	5746b	Isogeny class
Conductor	5746	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	1152	Modular degree for the optimal curve
Δ	-735488 = -1 · 28 · 132 · 17	Discriminant
Eigenvalues	2+ -1 -4  1 -4 13+ 17+ -2	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,23,5]	[a1,a2,a3,a4,a6]
Generators	[2:7:1]	Generators of the group modulo torsion
j	7433231/4352	j-invariant
L	1.420207612971	L(r)(E,1)/r!
Ω	1.6774082772527	Real period
R	0.4233339110789	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	45968j1 51714x1 5746h1 97682d1	Quadratic twists by: -4 -3 13 17

Hecke Eigenvalues for elliptic curve 5746b1

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
+	-1	-4	1	-4	+	+	-2	-7	10	5	-2	2	6	4	11	0	6	-8	-12	-2	-1	0	-1	12

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Quadratic twists for elliptic curve 5746b1

-4	-3	13	17
45968j1	51714x1	5746h1	97682d1

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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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