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
deg	912	Modular degree for the optimal curve
Δ	94931877133 = 377	Discriminant
Eigenvalues	0  1  0 -1  3  4 -6 -2	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-4563,116200]	[a1,a2,a3,a4,a6]
Generators	[170:1365:8]	Generators of the group modulo torsion
j	4096000/37	j-invariant
L	2.6378168817408	L(r)(E,1)/r!
Ω	1.0737110852008	Real period
R	0.61418218506317	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	21904h1 87616j1 12321c1 34225b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1369a1

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 1369a1

-4	8	-3	5	-7	37
21904h1	87616j1	12321c1	34225b1	67081a1	37b3

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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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