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	228a	Isogeny class
Conductor	228	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	18	Modular degree for the optimal curve
Δ	-155952 = -1 · 24 · 33 · 192	Discriminant
Eigenvalues	2- 3+  2  0  2  2  6 19+	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,3,18]	[a1,a2,a3,a4,a6]
j	131072/9747	j-invariant
L	1.2381939810832	L(r)(E,1)/r!
Ω	2.4763879621664	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	912j1 3648q1 684b1 5700j1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 228a1

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	2	2	6	+	2	4	-8	-2	-8	-8	2	-4	0	2	12	-4	6	-16	6	0	-2

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Quadratic twists for elliptic curve 228a1

-4	8	-3	5	-7	-11	13	17	-19	-23
912j1	3648q1	684b1	5700j1	11172v1	27588c1	38532g1	65892f1	4332c1	120612d1

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

Part of Computational Number Theory
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