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	16	Product of Tamagawa factors cp
Δ	122123738898 = 2 · 32 · 74 · 414	Discriminant
Eigenvalues	2- 3-  2 7+  0  6  2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-1812,24318]	[a1,a2,a3,a4,a6]
j	657980877056833/122123738898	j-invariant
L	3.9791943788839	L(r)(E,1)/r!
Ω	0.99479859472098	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	13776j4 55104g3 5166j4 43050h3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1722o3

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 1722o3

-4	8	-3	5	-7	41
13776j4	55104g3	5166j4	43050h3	12054bb4	70602u3

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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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