Cremona's table of elliptic curves

2299 = 11² · 19

Field	Data	Notes
Atkin-Lehner	11+ 19+	Signs for the Atkin-Lehner involutions
Class	2299a	Isogeny class
Conductor	2299	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	9504	Modular degree for the optimal curve
Δ	-851219116451 = -1 · 119 · 192	Discriminant
Eigenvalues	2 -3 -3  2 11+  2  6 19+	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,1331,-40263]	[a1,a2,a3,a4,a6]
Generators	[242:1327:8]	Generators of the group modulo torsion
j	110592/361	j-invariant
L	3.4141784430296	L(r)(E,1)/r!
Ω	0.45448440222407	Real period
R	1.878050394206	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	36784o1 20691j1 57475c1 112651g1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 2299a1

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 2299a1

-4	-3	5	-7	-11	-19
36784o1	20691j1	57475c1	112651g1	2299b1	43681g1

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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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