Cremona's table of elliptic curves

228 = 2² · 3 · 19

Field	Data	Notes
Atkin-Lehner	2- 3+ 19-	Signs for the Atkin-Lehner involutions
Class	228b	Isogeny class
Conductor	228	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	24	Modular degree for the optimal curve
Δ	-43776 = -1 · 28 · 32 · 19	Discriminant
Eigenvalues	2- 3+ -3  1 -5 -6 -5 19-	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,3,9]	[a1,a2,a3,a4,a6]
Generators	[3:-6:1]	Generators of the group modulo torsion
j	8192/171	j-invariant
L	1.2048427141293	L(r)(E,1)/r!
Ω	2.6951042086385	Real period
R	0.074508109325756	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	912i1 3648m1 684c1 5700m1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 228b1

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	1	-5	-6	-5	-	4	6	6	-8	-8	9	1	2	-8	11	0	-4	-11	-8	-4	10	-10

---

Quadratic twists for elliptic curve 228b1

-4	8	-3	5	-7	-11	13	17	-19	-23
912i1	3648m1	684c1	5700m1	11172q1	27588b1	38532d1	65892j1	4332d1	120612a1

---

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