Cremona's table of elliptic curves

1386 = 2 · 3² · 7 · 11

Field	Data	Notes
Atkin-Lehner	2- 3- 7+ 11+	Signs for the Atkin-Lehner involutions
Class	1386g	Isogeny class
Conductor	1386	Conductor
∏ cp	160	Product of Tamagawa factors cp
deg	3840	Modular degree for the optimal curve
Δ	11124486438912 = 220 · 39 · 72 · 11	Discriminant
Eigenvalues	2- 3- -2 7+ 11+  2 -6 -8	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-5801,57705]	[a1,a2,a3,a4,a6]
Generators	[-57:476:1]	Generators of the group modulo torsion
j	29609739866953/15259926528	j-invariant
L	3.444333330151	L(r)(E,1)/r!
Ω	0.63306255974186	Real period
R	0.54407471696881	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	11088bz1 44352bl1 462b1 34650z1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1386g1

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
-	-	-2	+	+	2	-6	-8	-4	-2	8	6	-6	8	-4	-10	-4	-14	-4	4	-14	-8	-4	14	18

---

Quadratic twists for elliptic curve 1386g1

-4	8	-3	5	-7	-11
11088bz1	44352bl1	462b1	34650z1	9702bv1	15246q1

---

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