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	1722a	Isogeny class
Conductor	1722	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	2160	Modular degree for the optimal curve
Δ	-69488911254 = -1 · 2 · 3 · 710 · 41	Discriminant
Eigenvalues	2+ 3+  3 7+ -4  1  3 -3	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-126,12642]	[a1,a2,a3,a4,a6]
Generators	[413:8197:1]	Generators of the group modulo torsion
j	-223980311017/69488911254	j-invariant
L	2.1285884598934	L(r)(E,1)/r!
Ω	0.89182670869782	Real period
R	1.1933868088574	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	13776t1 55104u1 5166be1 43050bx1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1722a1

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	+	-4	1	3	-3	-6	-8	-1	-8	+	-6	8	4	-3	4	1	-9	3	16	-11	-1	8

---

Quadratic twists for elliptic curve 1722a1

-4	8	-3	5	-7	41
13776t1	55104u1	5166be1	43050bx1	12054v1	70602k1

---

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