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	5746g	Isogeny class
Conductor	5746	Conductor
∏ cp	24	Product of Tamagawa factors cp
deg	32256	Modular degree for the optimal curve
Δ	1025967368261888 = 28 · 138 · 173	Discriminant
Eigenvalues	2+  0  4  2  2 13+ 17-  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-29015,-1108067]	[a1,a2,a3,a4,a6]
j	559679941521/212556032	j-invariant
L	2.2659977865807	L(r)(E,1)/r!
Ω	0.37766629776345	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	45968q1 51714r1 442b1 97682c1	Quadratic twists by: -4 -3 13 17

Hecke Eigenvalues for elliptic curve 5746g1

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	4	2	2	+	-	0	-4	2	2	0	0	4	8	-6	-8	-2	-16	14	16	8	12	18	4

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Quadratic twists for elliptic curve 5746g1

-4	-3	13	17
45968q1	51714r1	442b1	97682c1

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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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