Cremona's table of elliptic curves

249 = 3 · 83

Field	Data	Notes
Atkin-Lehner	3+ 83+	Signs for the Atkin-Lehner involutions
Class	249b	Isogeny class
Conductor	249	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	8	Modular degree for the optimal curve
Δ	-249 = -1 · 3 · 83	Discriminant
Eigenvalues	1 3+ -1 -4 -3  2  4 -1	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,2,1]	[a1,a2,a3,a4,a6]
Generators	[0:1:1]	Generators of the group modulo torsion
j	357911/249	j-invariant
L	1.5162589106946	L(r)(E,1)/r!
Ω	3.5061259800005	Real period
R	0.43245990570321	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	3984g1 15936l1 747e1 6225i1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 249b1

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	-4	-3	2	4	-1	-3	4	-6	-9	-2	4	8	7	-9	-13	5	0	-12	-12	+	9	-6

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Quadratic twists for elliptic curve 249b1

-4	8	-3	5	-7	-11	13	17	-19	-83
3984g1	15936l1	747e1	6225i1	12201k1	30129g1	42081b1	71961c1	89889g1	20667e1

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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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