Cremona's table of elliptic curves

209 = 11 · 19

Field	Data	Notes
Atkin-Lehner	11- 19-	Signs for the Atkin-Lehner involutions
Class	209a	Isogeny class
Conductor	209	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	24	Modular degree for the optimal curve
Δ	-480491 = -1 · 113 · 192	Discriminant
Eigenvalues	0  1 -3 -4 11-  2  0 19-	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-27,55]	[a1,a2,a3,a4,a6]
Generators	[-5:9:1]	Generators of the group modulo torsion
j	-2258403328/480491	j-invariant
L	1.252324140818	L(r)(E,1)/r!
Ω	2.8242928435156	Real period
R	0.66511736399426	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	3344e1 13376c1 1881b1 5225c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 209a1

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	-3	-4	-	2	0	-	3	-6	-7	-7	0	-10	0	6	3	-10	11	15	8	-16	0	9	-1

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Quadratic twists for elliptic curve 209a1

-4	8	-3	5	-7	-11	13	17	-19	-23
3344e1	13376c1	1881b1	5225c1	10241e1	2299c1	35321a1	60401b1	3971a1	110561a1

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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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