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	222c	Isogeny class
Conductor	222	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	36	Modular degree for the optimal curve
Δ	-255744 = -1 · 28 · 33 · 37	Discriminant
Eigenvalues	2+ 3+  2  0 -4  6  6  8	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,16,0]	[a1,a2,a3,a4,a6]
j	410172407/255744	j-invariant
L	0.89650114973835	L(r)(E,1)/r!
Ω	1.7930022994767	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	1776j1 7104g1 666f1 5550bf1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 222c1

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	6	6	8	0	-6	4	-	-6	-8	8	6	-4	-2	-12	0	10	-12	-4	-10	-6

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Quadratic twists for elliptic curve 222c1

-4	8	-3	5	-7	-11	13	17	-19	-23	37
1776j1	7104g1	666f1	5550bf1	10878s1	26862m1	37518k1	64158p1	80142v1	117438b1	8214g1

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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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