Cremona's table of elliptic curves

1369 = 37²

Field	Data	Notes
Atkin-Lehner	37+	Signs for the Atkin-Lehner involutions
Class	1369b	Isogeny class
Conductor	1369	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	1332	Modular degree for the optimal curve
Δ	-3512479453921 = -1 · 378	Discriminant
Eigenvalues	1  0  1  2 -2 -2  3 -6	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,3166,-59359]	[a1,a2,a3,a4,a6]
Generators	[7924:91377:64]	Generators of the group modulo torsion
j	999	j-invariant
L	3.3668281888319	L(r)(E,1)/r!
Ω	0.43019373262151	Real period
R	7.8263069252896	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	21904e1 87616b1 12321e1 34225e1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1369b1

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
1	0	1	2	-2	-2	3	-6	-4	9	-10	+	-9	2	6	-2	-4	1	-10	6	-10	10	-12	7	7

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Quadratic twists for elliptic curve 1369b1

-4	8	-3	5	-7	37
21904e1	87616b1	12321e1	34225e1	67081b1	1369c1

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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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