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	2409f	Isogeny class
Conductor	2409	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	560	Modular degree for the optimal curve
Δ	715473 = 34 · 112 · 73	Discriminant
Eigenvalues	-1 3-  2 -4 11-  6 -2  4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-187,968]	[a1,a2,a3,a4,a6]
j	723425270833/715473	j-invariant
L	1.4204767190353	L(r)(E,1)/r!
Ω	2.8409534380707	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	38544i1 7227e1 60225f1 118041d1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 2409f1

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	-	2	-4	-	6	-2	4	0	2	4	-10	-6	8	0	2	-4	-2	-4	8	-	16	12	10	18

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Quadratic twists for elliptic curve 2409f1

-4	-3	5	-7	-11
38544i1	7227e1	60225f1	118041d1	26499i1

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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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