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
Δ	-517504691 = -1 · 11 · 196	Discriminant
Eigenvalues	0  1 -3 -4 11-  2  0 19-	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,193,-308]	[a1,a2,a3,a4,a6]
Generators	[2:9:1]	Generators of the group modulo torsion
j	790939860992/517504691	j-invariant
L	1.252324140818	L(r)(E,1)/r!
Ω	0.94143094783853	Real period
R	0.22170578799809	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	3344e2 13376c2 1881b2 5225c2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 209a2

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 209a2

-4	8	-3	5	-7	-11	13	17	-19	-23
3344e2	13376c2	1881b2	5225c2	10241e2	2299c2	35321a2	60401b2	3971a2	110561a2

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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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