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	1722q	Isogeny class
Conductor	1722	Conductor
∏ cp	9	Product of Tamagawa factors cp
deg	264	Modular degree for the optimal curve
Δ	-61992 = -1 · 23 · 33 · 7 · 41	Discriminant
Eigenvalues	2- 3-  0 7- -3 -4  6  5	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-28,56]	[a1,a2,a3,a4,a6]
j	-2433138625/61992	j-invariant
L	3.4942339405355	L(r)(E,1)/r!
Ω	3.4942339405355	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	13776d1 55104k1 5166q1 43050a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1722q1

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
-	-	0	-	-3	-4	6	5	9	6	5	2	+	11	-3	-12	-9	5	2	-12	-4	-13	-12	6	-13

---

Quadratic twists for elliptic curve 1722q1

-4	8	-3	5	-7	41
13776d1	55104k1	5166q1	43050a1	12054be1	70602n1

---

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