Cremona's table of elliptic curves

2222 = 2 · 11 · 101

Field	Data	Notes
Atkin-Lehner	2- 11+ 101+	Signs for the Atkin-Lehner involutions
Class	2222a	Isogeny class
Conductor	2222	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	1424	Modular degree for the optimal curve
Δ	-97768 = -1 · 23 · 112 · 101	Discriminant
Eigenvalues	2- -2  0 -1 11+ -4  3  5	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-5853,171865]	[a1,a2,a3,a4,a6]
j	-22175014984908625/97768	j-invariant
L	1.5142994139059	L(r)(E,1)/r!
Ω	2.2714491208588	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	17776g1 71104i1 19998j1 55550c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2222a1

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	0	-1	+	-4	3	5	0	3	-4	2	12	-1	6	9	6	-13	14	6	2	14	-6	-6	17

---

Quadratic twists for elliptic curve 2222a1

-4	8	-3	5	-7	-11
17776g1	71104i1	19998j1	55550c1	108878o1	24442f1

---

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