Cremona's table of elliptic curves

1665 = 3² · 5 · 37

Field	Data	Notes
Atkin-Lehner	3- 5+ 37-	Signs for the Atkin-Lehner involutions
Class	1665c	Isogeny class
Conductor	1665	Conductor
∏ cp	12	Product of Tamagawa factors cp
Δ	-44865134955 = -1 · 311 · 5 · 373	Discriminant
Eigenvalues	0 3- 5+  2  0 -1 -6  2	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-1771248,907333974]	[a1,a2,a3,a4,a6]
Generators	[878:5386:1]	Generators of the group modulo torsion
j	-843013059301831868416/61543395	j-invariant
L	2.4204343293128	L(r)(E,1)/r!
Ω	0.63001407965824	Real period
R	2.8814050441053	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	26640bf2 106560co2 555b2 8325r2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1665c2

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

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Quadratic twists for elliptic curve 1665c2

-4	8	-3	5	-7	37
26640bf2	106560co2	555b2	8325r2	81585z2	61605i2

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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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