Cremona's table of elliptic curves

2299 = 11² · 19

Field	Data	Notes
Atkin-Lehner	11- 19+	Signs for the Atkin-Lehner involutions
Class	2299d	Isogeny class
Conductor	2299	Conductor
∏ cp	1	Product of Tamagawa factors cp
Δ	-12151136899 = -1 · 116 · 193	Discriminant
Eigenvalues	0 -2  3  1 11-  4  3 19+	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-1129,15164]	[a1,a2,a3,a4,a6]
j	-89915392/6859	j-invariant
L	1.2443651762233	L(r)(E,1)/r!
Ω	1.2443651762233	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	36784bj2 20691o2 57475h2 112651l2	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 2299d2

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	-2	3	1	-	4	3	+	0	-6	-4	2	6	1	-3	12	-6	1	-4	6	7	-8	-12	12	8

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Quadratic twists for elliptic curve 2299d2

-4	-3	5	-7	-11	-19
36784bj2	20691o2	57475h2	112651l2	19a1	43681j2

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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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