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	5746h	Isogeny class
Conductor	5746	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	14976	Modular degree for the optimal curve
Δ	-3550060097792 = -1 · 28 · 138 · 17	Discriminant
Eigenvalues	2- -1  4 -1  4 13+ 17+  2	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,3799,-8169]	[a1,a2,a3,a4,a6]
j	7433231/4352	j-invariant
L	3.7218348021675	L(r)(E,1)/r!
Ω	0.46522935027094	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	45968i1 51714j1 5746b1 97682l1	Quadratic twists by: -4 -3 13 17

Hecke Eigenvalues for elliptic curve 5746h1

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 5746h1

-4	-3	13	17
45968i1	51714j1	5746b1	97682l1

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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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