Cremona's table of elliptic curves

249 = 3 · 83

Field	Data	Notes
Atkin-Lehner	3+ 83+	Signs for the Atkin-Lehner involutions
Class	249a	Isogeny class
Conductor	249	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	24	Modular degree for the optimal curve
Δ	-2241 = -1 · 33 · 83	Discriminant
Eigenvalues	-1 3+  1  0 -3 -6 -4 -7	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-55,134]	[a1,a2,a3,a4,a6]
Generators	[4:-3:1]	Generators of the group modulo torsion
j	-18420660721/2241	j-invariant
L	0.98375962031742	L(r)(E,1)/r!
Ω	4.4420811152244	Real period
R	0.22146367767706	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	3984f1 15936m1 747c1 6225h1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 249a1

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	0	-3	-6	-4	-7	5	8	-10	7	-2	4	-12	9	-1	11	-5	-4	12	-4	+	-9	-2

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Quadratic twists for elliptic curve 249a1

-4	8	-3	5	-7	-11	13	17	-19	-83
3984f1	15936m1	747c1	6225h1	12201m1	30129e1	42081a1	71961d1	89889e1	20667c1

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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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