Cremona's table of elliptic curves

1089 = 3² · 11²

Field	Data	Notes
Atkin-Lehner	3- 11-	Signs for the Atkin-Lehner involutions
Class	1089f	Isogeny class
Conductor	1089	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	144	Modular degree for the optimal curve
Δ	-88209 = -1 · 36 · 112	Discriminant
Eigenvalues	1 3- -1  2 11- -1 -5 -6	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-270,1777]	[a1,a2,a3,a4,a6]
Generators	[8:5:1]	Generators of the group modulo torsion
j	-24729001	j-invariant
L	2.9805147699195	L(r)(E,1)/r!
Ω	3.1904476027225	Real period
R	0.46709978364418	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	17424bu1 69696bo1 121a1 27225bm1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1089f1

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	-	-1	2	-	-1	-5	-6	-2	9	-2	-3	-5	0	-2	-9	-8	-6	2	-12	2	10	6	9	-13

---

Quadratic twists for elliptic curve 1089f1

-4	8	-3	5	-7	-11
17424bu1	69696bo1	121a1	27225bm1	53361bh1	1089h2

---

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