Cremona's table of elliptic curves

2299 = 11² · 19

Field	Data	Notes
Atkin-Lehner	11+ 19-	Signs for the Atkin-Lehner involutions
Class	2299b	Isogeny class
Conductor	2299	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	864	Modular degree for the optimal curve
Δ	-480491 = -1 · 113 · 192	Discriminant
Eigenvalues	-2 -3 -3 -2 11+ -2 -6 19-	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,11,30]	[a1,a2,a3,a4,a6]
Generators	[0:5:1] [3:9:1]	Generators of the group modulo torsion
j	110592/361	j-invariant
L	1.1976598231395	L(r)(E,1)/r!
Ω	2.0877183400457	Real period
R	0.14341731355291	Regulator
r	2	Rank of the group of rational points
S	1.0000000000012	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	36784l1 20691l1 57475f1 112651e1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 2299b1

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
-2	-3	-3	-2	+	-2	-6	-	3	10	1	-11	-8	-4	-8	-6	-1	-14	-13	-13	4	-10	6	-7	-9

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Quadratic twists for elliptic curve 2299b1

-4	-3	5	-7	-11	-19
36784l1	20691l1	57475f1	112651e1	2299a1	43681f1

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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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