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	1722n	Isogeny class
Conductor	1722	Conductor
∏ cp	70	Product of Tamagawa factors cp
deg	560	Modular degree for the optimal curve
Δ	-62487936 = -1 · 27 · 35 · 72 · 41	Discriminant
Eigenvalues	2- 3- -3 7+  0 -5 -1 -1	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-32,384]	[a1,a2,a3,a4,a6]
Generators	[-2:22:1]	Generators of the group modulo torsion
j	-3630961153/62487936	j-invariant
L	4.0281152763361	L(r)(E,1)/r!
Ω	1.6595397150529	Real period
R	0.034674978505003	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	13776h1 55104b1 5166n1 43050d1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1722n1

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	+	0	-5	-1	-1	-2	0	-9	-8	+	6	-8	0	3	0	-5	3	3	-4	-5	3	-8

---

Quadratic twists for elliptic curve 1722n1

-4	8	-3	5	-7	41
13776h1	55104b1	5166n1	43050d1	12054bf1	70602x1

---

Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
Back to Tables and computations