Cremona's table of elliptic curves

2499 = 3 · 7² · 17

Field	Data	Notes
Atkin-Lehner	3+ 7- 17+	Signs for the Atkin-Lehner involutions
Class	2499c	Isogeny class
Conductor	2499	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	7560	Modular degree for the optimal curve
Δ	337235618295891 = 35 · 710 · 173	Discriminant
Eigenvalues	-1 3+ -1 7- -2 -1 17+  8	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-26461,1390472]	[a1,a2,a3,a4,a6]
j	7253758561/1193859	j-invariant
L	0.51652268182266	L(r)(E,1)/r!
Ω	0.51652268182266	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	39984db1 7497n1 62475cc1 2499i1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 2499c1

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	+	-1	-	-2	-1	+	8	0	-5	-3	0	7	-4	-9	0	3	-4	-8	0	6	8	9	2	12

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Quadratic twists for elliptic curve 2499c1

-4	-3	5	-7	17
39984db1	7497n1	62475cc1	2499i1	42483u1

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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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