Cremona's table of elliptic curves

2739 = 3 · 11 · 83

Field	Data	Notes
Atkin-Lehner	3+ 11+ 83+	Signs for the Atkin-Lehner involutions
Class	2739b	Isogeny class
Conductor	2739	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	864	Modular degree for the optimal curve
Δ	-2982771 = -1 · 33 · 113 · 83	Discriminant
Eigenvalues	2 3+  1  0 11+ -6  5 -7	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-120,-475]	[a1,a2,a3,a4,a6]
Generators	[3578:75557:8]	Generators of the group modulo torsion
j	-192699928576/2982771	j-invariant
L	5.4025056464461	L(r)(E,1)/r!
Ω	0.72006818796146	Real period
R	7.5027695109554	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	43824bl1 8217m1 68475f1 30129k1	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 2739b1

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	+	1	0	+	-6	5	-7	2	-1	-4	-11	10	1	0	3	8	2	4	11	-9	-13	+	-18	-2

---

Quadratic twists for elliptic curve 2739b1

-4	-3	5	-11
43824bl1	8217m1	68475f1	30129k1

---

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