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	1722h	Isogeny class
Conductor	1722	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	1440	Modular degree for the optimal curve
Δ	-55601051856 = -1 · 24 · 3 · 75 · 413	Discriminant
Eigenvalues	2- 3+  1 7+  2  3  2  2	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,920,-3271]	[a1,a2,a3,a4,a6]
j	86110813111679/55601051856	j-invariant
L	2.556560092286	L(r)(E,1)/r!
Ω	0.63914002307151	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	13776s1 55104s1 5166m1 43050q1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1722h1

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
-	+	1	+	2	3	2	2	-7	7	0	5	+	2	9	3	4	6	1	-10	16	-3	14	-12	-5

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Quadratic twists for elliptic curve 1722h1

-4	8	-3	5	-7	41
13776s1	55104s1	5166m1	43050q1	12054bl1	70602bk1

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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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