Cremona's table of elliptic curves

2299 = 11² · 19

Field	Data	Notes
Atkin-Lehner	11- 19+	Signs for the Atkin-Lehner involutions
Class	2299c	Isogeny class
Conductor	2299	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	2880	Modular degree for the optimal curve
Δ	-851219116451 = -1 · 119 · 192	Discriminant
Eigenvalues	0  1 -3  4 11- -2  0 19+	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-3307,-86718]	[a1,a2,a3,a4,a6]
j	-2258403328/480491	j-invariant
L	1.2449169737712	L(r)(E,1)/r!
Ω	0.31122924344279	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	36784bi1 20691n1 57475g1 112651j1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 2299c1

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

---

Quadratic twists for elliptic curve 2299c1

-4	-3	5	-7	-11	-19
36784bi1	20691n1	57475g1	112651j1	209a1	43681i1

---

Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
Back to Tables and computations