Cremona's table of elliptic curves

222 = 2 · 3 · 37

Field	Data	Notes
Atkin-Lehner	2- 3- 37-	Signs for the Atkin-Lehner involutions
Class	222a	Isogeny class
Conductor	222	Conductor
∏ cp	9	Product of Tamagawa factors cp
deg	12	Modular degree for the optimal curve
Δ	-7992 = -1 · 23 · 33 · 37	Discriminant
Eigenvalues	2- 3-  0 -1  3 -1 -3 -7	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,2,-4]	[a1,a2,a3,a4,a6]
j	857375/7992	j-invariant
L	2.0529956743308	L(r)(E,1)/r!
Ω	2.0529956743308	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	1776g1 7104a1 666c1 5550a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 222a1

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
-	-	0	-1	3	-1	-3	-7	3	0	2	-	-6	-4	6	9	0	-10	2	12	5	2	3	-3	2

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Quadratic twists for elliptic curve 222a1

-4	8	-3	5	-7	-11	13	17	-19	-23	37
1776g1	7104a1	666c1	5550a1	10878bh1	26862h1	37518f1	64158z1	80142d1	117438q1	8214d1

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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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