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	2409b	Isogeny class
Conductor	2409	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	12800	Modular degree for the optimal curve
Δ	-7484100287210019 = -1 · 325 · 112 · 73	Discriminant
Eigenvalues	0 3+ -1  2 11+  4  3 -7	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-152241,-23188750]	[a1,a2,a3,a4,a6]
j	-390230714139735752704/7484100287210019	j-invariant
L	0.96567860355408	L(r)(E,1)/r!
Ω	0.12070982544426	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	4	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	38544q1 7227h1 60225p1 118041g1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 2409b1

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	+	-1	2	+	4	3	-7	-2	-6	4	5	-2	6	-5	-1	5	1	7	6	-	5	15	8	9

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Quadratic twists for elliptic curve 2409b1

-4	-3	5	-7	-11
38544q1	7227h1	60225p1	118041g1	26499a1

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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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