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	222b	Isogeny class
Conductor	222	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	44	Modular degree for the optimal curve
Δ	-13108878 = -1 · 2 · 311 · 37	Discriminant
Eigenvalues	2- 3+  0  3  1  1 -3  3	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,17,179]	[a1,a2,a3,a4,a6]
j	541343375/13108878	j-invariant
L	1.6808078275302	L(r)(E,1)/r!
Ω	1.6808078275302	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	1776i1 7104k1 666b1 5550q1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 222b1

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	3	1	1	-3	3	-1	-4	-6	+	-10	12	-6	-1	0	2	2	0	-3	14	9	-3	-10

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Quadratic twists for elliptic curve 222b1

-4	8	-3	5	-7	-11	13	17	-19	-23	37
1776i1	7104k1	666b1	5550q1	10878bo1	26862b1	37518d1	64158bm1	80142j1	117438n1	8214a1

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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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