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	1722b	Isogeny class
Conductor	1722	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	288	Modular degree for the optimal curve
Δ	-13776 = -1 · 24 · 3 · 7 · 41	Discriminant
Eigenvalues	2+ 3+ -3 7+  2  1 -6  6	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-44,96]	[a1,a2,a3,a4,a6]
Generators	[4:0:1]	Generators of the group modulo torsion
j	-9759185353/13776	j-invariant
L	1.5381921560264	L(r)(E,1)/r!
Ω	3.9624980166922	Real period
R	0.1940937445958	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	13776u1 55104t1 5166bd1 43050bv1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1722b1

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
+	+	-3	+	2	1	-6	6	3	1	8	-11	+	6	-7	13	0	-2	-11	-6	0	1	-14	-16	-7

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Quadratic twists for elliptic curve 1722b1

-4	8	-3	5	-7	41
13776u1	55104t1	5166bd1	43050bv1	12054t1	70602l1

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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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