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	5746a	Isogeny class
Conductor	5746	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-3029193317470346 = -1 · 2 · 137 · 176	Discriminant
Eigenvalues	2+  0 -2 -4  2 13+ 17+  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,6137,2640015]	[a1,a2,a3,a4,a6]
Generators	[-81:1308:1]	Generators of the group modulo torsion
j	5295319407/627576794	j-invariant
L	1.9631540001101	L(r)(E,1)/r!
Ω	0.3458910597267	Real period
R	2.8378212516698	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	45968h2 51714t2 442a2 97682b2	Quadratic twists by: -4 -3 13 17

Hecke Eigenvalues for elliptic curve 5746a2

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
+	0	-2	-4	2	+	+	0	2	8	8	6	-12	4	8	-6	4	-8	8	8	-8	-10	0	-6	16

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Quadratic twists for elliptic curve 5746a2

-4	-3	13	17
45968h2	51714t2	442a2	97682b2

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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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