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	2	Product of Tamagawa factors cp
Δ	5166 = 2 · 32 · 7 · 41	Discriminant
Eigenvalues	2- 3-  2 7+  0  6  2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-27552,1757970]	[a1,a2,a3,a4,a6]
j	2313045024604457473/5166	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	4	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	13776j3 55104g4 5166j3 43050h4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1722o4

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 1722o4

-4	8	-3	5	-7	41
13776j3	55104g4	5166j3	43050h4	12054bb3	70602u4

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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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