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	2706q	Isogeny class
Conductor	2706	Conductor
∏ cp	12	Product of Tamagawa factors cp
Δ	357192 = 23 · 32 · 112 · 41	Discriminant
Eigenvalues	2- 3- -4  2 11+ -2 -6  0	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-1750,-28324]	[a1,a2,a3,a4,a6]
Generators	[50:74:1]	Generators of the group modulo torsion
j	592725168252001/357192	j-invariant
L	4.6434047091703	L(r)(E,1)/r!
Ω	0.7381400427926	Real period
R	2.0968941935024	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	21648v2 86592t2 8118j2 67650d2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2706q2

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

---

Quadratic twists for elliptic curve 2706q2

-4	8	-3	5	-11	41
21648v2	86592t2	8118j2	67650d2	29766x2	110946ba2

---

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