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	1722k	Isogeny class
Conductor	1722	Conductor
∏ cp	114	Product of Tamagawa factors cp
deg	4560	Modular degree for the optimal curve
Δ	-5311764627456 = -1 · 219 · 3 · 72 · 413	Discriminant
Eigenvalues	2- 3+  1 7+ -4 -3 -7  5	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-5425,187343]	[a1,a2,a3,a4,a6]
Generators	[-53:600:1]	Generators of the group modulo torsion
j	-17657448289261201/5311764627456	j-invariant
L	3.5894913259769	L(r)(E,1)/r!
Ω	0.723581041983	Real period
R	0.043515189302156	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	13776z1 55104bb1 5166i1 43050w1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1722k1

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
-	+	1	+	-4	-3	-7	5	2	-8	-9	8	-	2	0	0	-5	-12	-11	5	7	12	11	-3	-8

---

Quadratic twists for elliptic curve 1722k1

-4	8	-3	5	-7	41
13776z1	55104bb1	5166i1	43050w1	12054bh1	70602bl1

---

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