Cremona's table of elliptic curves

1369 = 37²

Field	Data	Notes
Atkin-Lehner	37-	Signs for the Atkin-Lehner involutions
Class	1369f	Isogeny class
Conductor	1369	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	5328	Modular degree for the optimal curve
Δ	129961739795077 = 379	Discriminant
Eigenvalues	-2  1 -2  3  3 -6  2  6	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-16884,-647702]	[a1,a2,a3,a4,a6]
j	4096	j-invariant
L	0.85255645319845	L(r)(E,1)/r!
Ω	0.42627822659923	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	21904o1 87616r1 12321i1 34225j1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1369f1

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
-2	1	-2	3	3	-6	2	6	4	4	0	-	3	-6	3	9	-4	0	12	-3	-9	6	9	14	12

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Quadratic twists for elliptic curve 1369f1

-4	8	-3	5	-7	37
21904o1	87616r1	12321i1	34225j1	67081j1	1369e1

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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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