Cremona's table of elliptic curves

1722 = 2 · 3 · 7 · 41

Field	Data	Notes
Atkin-Lehner	2- 3- 7+ 41-	Signs for the Atkin-Lehner involutions
Class	1722o	Isogeny class
Conductor	1722	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	26687556 = 22 · 34 · 72 · 412	Discriminant
Eigenvalues	2- 3-  2 7+  0  6  2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-1722,27360]	[a1,a2,a3,a4,a6]
j	564727473247393/26687556	j-invariant
L	3.9791943788839	L(r)(E,1)/r!
Ω	1.989597189442	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	13776j2 55104g2 5166j2 43050h2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1722o2

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	6	2	-4	0	2	-8	6	-	4	-8	-6	0	10	8	8	-6	-16	0	10	2

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Quadratic twists for elliptic curve 1722o2

-4	8	-3	5	-7	41
13776j2	55104g2	5166j2	43050h2	12054bb2	70602u2

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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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