Cremona's table of elliptic curves

2242 = 2 · 19 · 59

Field	Data	Notes
Atkin-Lehner	2- 19- 59+	Signs for the Atkin-Lehner involutions
Class	2242a	Isogeny class
Conductor	2242	Conductor
∏ cp	10	Product of Tamagawa factors cp
deg	320	Modular degree for the optimal curve
Δ	-681568 = -1 · 25 · 192 · 59	Discriminant
Eigenvalues	2- -2  0 -3  3 -1  3 19-	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,22,4]	[a1,a2,a3,a4,a6]
Generators	[6:16:1]	Generators of the group modulo torsion
j	1174241375/681568	j-invariant
L	3.152394140994	L(r)(E,1)/r!
Ω	1.7245738444731	Real period
R	0.18279264475086	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	17936c1 71744b1 20178h1 56050c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2242a1

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	-3	3	-1	3	-	6	-6	-6	-5	7	-11	-2	-2	+	-10	4	3	-16	-11	-9	-4	-12

---

Quadratic twists for elliptic curve 2242a1

-4	8	-3	5	-7	-19
17936c1	71744b1	20178h1	56050c1	109858p1	42598c1

---

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