Cremona's table of elliptic curves

2409 = 3 · 11 · 73

Field	Data	Notes
Atkin-Lehner	3- 11+ 73+	Signs for the Atkin-Lehner involutions
Class	2409d	Isogeny class
Conductor	2409	Conductor
∏ cp	14	Product of Tamagawa factors cp
deg	1568	Modular degree for the optimal curve
Δ	-19317771 = -1 · 37 · 112 · 73	Discriminant
Eigenvalues	-2 3- -3 -4 11+ -6 -7 -7	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-32,212]	[a1,a2,a3,a4,a6]
Generators	[-8:4:1] [-5:16:1]	Generators of the group modulo torsion
j	-3738308608/19317771	j-invariant
L	2.0222982992484	L(r)(E,1)/r!
Ω	1.8801470492225	Real period
R	0.076829032376709	Regulator
r	2	Rank of the group of rational points
S	1.0000000000003	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	38544m1 7227f1 60225d1 118041b1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 2409d1

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	-	-3	-4	+	-6	-7	-7	-4	2	8	-7	-4	-6	5	9	-9	-7	-13	-4	+	1	9	12	-19

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Quadratic twists for elliptic curve 2409d1

-4	-3	5	-7	-11
38544m1	7227f1	60225d1	118041b1	26499m1

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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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