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	2499f	Isogeny class
Conductor	2499	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	2304	Modular degree for the optimal curve
Δ	-84967401939 = -1 · 3 · 78 · 173	Discriminant
Eigenvalues	2 3+ -1 7-  1 -1 17- -1	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,964,7685]	[a1,a2,a3,a4,a6]
Generators	[26:829:8]	Generators of the group modulo torsion
j	841232384/722211	j-invariant
L	4.9185990293714	L(r)(E,1)/r!
Ω	0.7002306822974	Real period
R	1.1707092042949	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	39984dp1 7497j1 62475by1 357c1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 2499f1

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	+	-1	-	1	-1	-	-1	-3	-2	0	-6	1	5	-12	0	0	2	-8	0	-6	-4	-6	-16	12

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Quadratic twists for elliptic curve 2499f1

-4	-3	5	-7	17
39984dp1	7497j1	62475by1	357c1	42483w1

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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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