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	94931877133 = 377	Discriminant
Eigenvalues	0  1  0 -1  3  4 -6 -2	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-2564593,-1581651042]	[a1,a2,a3,a4,a6]
Generators	[-265909974:-145117:287496]	Generators of the group modulo torsion
j	727057727488000/37	j-invariant
L	2.6378168817408	L(r)(E,1)/r!
Ω	0.11930123168898	Real period
R	5.5276396655686	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	21904h3 87616j3 12321c3 34225b3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1369a3

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 1369a3

-4	8	-3	5	-7	37
21904h3	87616j3	12321c3	34225b3	67081a3	37b2

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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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