Cremona's table of elliptic curves

2204 = 2² · 19 · 29

Field	Data	Notes
Atkin-Lehner	2- 19+ 29+	Signs for the Atkin-Lehner involutions
Class	2204a	Isogeny class
Conductor	2204	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	1248	Modular degree for the optimal curve
Δ	-967503104 = -1 · 28 · 194 · 29	Discriminant
Eigenvalues	2-  3  3  0 -3  1  2 19+	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-31,-1498]	[a1,a2,a3,a4,a6]
j	-12869712/3779309	j-invariant
L	4.2038890082044	L(r)(E,1)/r!
Ω	0.70064816803406	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	8816h1 35264r1 19836e1 55100b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2204a1

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
-	3	3	0	-3	1	2	+	-2	+	7	-4	0	9	3	-9	6	-6	-4	6	8	9	-2	-12	-12

---

Quadratic twists for elliptic curve 2204a1

-4	8	-3	5	-7	-19	29
8816h1	35264r1	19836e1	55100b1	107996g1	41876f1	63916i1

---

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