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	1722l	Isogeny class
Conductor	1722	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	1920	Modular degree for the optimal curve
Δ	-610094268 = -1 · 22 · 312 · 7 · 41	Discriminant
Eigenvalues	2- 3+ -4 7+  6  2 -2  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-480,-4419]	[a1,a2,a3,a4,a6]
Generators	[537:12179:1]	Generators of the group modulo torsion
j	-12232183057921/610094268	j-invariant
L	3.0325270985531	L(r)(E,1)/r!
Ω	0.50850364365809	Real period
R	5.9636290444993	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	13776bd1 55104bf1 5166k1 43050y1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1722l1

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
-	+	-4	+	6	2	-2	0	-8	-8	-4	-2	-	-8	0	0	-10	-12	14	0	2	-8	-14	2	2

---

Quadratic twists for elliptic curve 1722l1

-4	8	-3	5	-7	41
13776bd1	55104bf1	5166k1	43050y1	12054bi1	70602br1

---

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