Cremona's table of elliptic curves

2706 = 2 · 3 · 11 · 41

Field	Data	Notes
Atkin-Lehner	2+ 3- 11- 41+	Signs for the Atkin-Lehner involutions
Class	2706g	Isogeny class
Conductor	2706	Conductor
∏ cp	18	Product of Tamagawa factors cp
deg	5760	Modular degree for the optimal curve
Δ	1508779008 = 210 · 33 · 113 · 41	Discriminant
Eigenvalues	2+ 3-  0 -4 11-  2  6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-30686,2066384]	[a1,a2,a3,a4,a6]
Generators	[222:2380:1]	Generators of the group modulo torsion
j	3195392484115617625/1508779008	j-invariant
L	2.6810599749715	L(r)(E,1)/r!
Ω	1.2328001922365	Real period
R	4.3495450306633	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	6	Number of elements in the torsion subgroup
Twists	21648m1 86592a1 8118k1 67650by1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2706g1

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

---

Quadratic twists for elliptic curve 2706g1

-4	8	-3	5	-11	41
21648m1	86592a1	8118k1	67650by1	29766bq1	110946a1

---

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