Cremona's table of elliptic curves

888 = 2³ · 3 · 37

Field	Data	Notes
Atkin-Lehner	2+ 3- 37-	Signs for the Atkin-Lehner involutions
Class	888b	Isogeny class
Conductor	888	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	340992 = 210 · 32 · 37	Discriminant
Eigenvalues	2+ 3- -2  0 -4 -2 -6  0	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-7104,-232848]	[a1,a2,a3,a4,a6]
Generators	[147:1386:1]	Generators of the group modulo torsion
j	38725206845188/333	j-invariant
L	2.4590584169849	L(r)(E,1)/r!
Ω	0.52001841393768	Real period
R	4.7287910410027	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	1776a3 7104b3 2664g3 22200l4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 888b3

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	-4	-2	-6	0	-4	6	4	-	-6	-8	-8	6	0	14	4	-16	-6	-4	-4	18	2

---

Quadratic twists for elliptic curve 888b3

-4	8	-3	5	-7	-11	37
1776a3	7104b3	2664g3	22200l4	43512c4	107448bd4	32856m4

---

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