Cremona's table of elliptic curves

1369 = 37²

Field	Data	Notes
Atkin-Lehner	37+	Signs for the Atkin-Lehner involutions
Class	1369a	Isogeny class
Conductor	1369	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	129961739795077 = 379	Discriminant
Eigenvalues	0  1  0 -1  3  4 -6 -2	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-31943,-2138543]	[a1,a2,a3,a4,a6]
Generators	[-23826:50545:216]	Generators of the group modulo torsion
j	1404928000/50653	j-invariant
L	2.6378168817408	L(r)(E,1)/r!
Ω	0.35790369506694	Real period
R	1.8425465551895	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	21904h2 87616j2 12321c2 34225b2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1369a2

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	1	0	-1	3	4	-6	-2	-6	6	4	+	-9	-8	3	-3	-12	-8	-4	-15	11	10	9	-6	-8

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Quadratic twists for elliptic curve 1369a2

-4	8	-3	5	-7	37
21904h2	87616j2	12321c2	34225b2	67081a2	37b1

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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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