Properties

Label 1089.j
Number of curves $4$
Conductor $1089$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("j1")
 
E.isogeny_class()
 

Elliptic curves in class 1089.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1089.j1 1089g3 \([1, -1, 0, -159561, 24548134]\) \(347873904937/395307\) \(510526328421483\) \([2]\) \(5760\) \(1.7356\)  
1089.j2 1089g2 \([1, -1, 0, -12546, 173047]\) \(169112377/88209\) \(113919098077521\) \([2, 2]\) \(2880\) \(1.3890\)  
1089.j3 1089g1 \([1, -1, 0, -7101, -226616]\) \(30664297/297\) \(383565986793\) \([2]\) \(1440\) \(1.0425\) \(\Gamma_0(N)\)-optimal
1089.j4 1089g4 \([1, -1, 0, 47349, 1311052]\) \(9090072503/5845851\) \(-7549729318046619\) \([2]\) \(5760\) \(1.7356\)  

Rank

sage: E.rank()
 

The elliptic curves in class 1089.j have rank \(1\).

Complex multiplication

The elliptic curves in class 1089.j do not have complex multiplication.

Modular form 1089.2.a.j

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{4} + 2 q^{5} - 4 q^{7} - 3 q^{8} + 2 q^{10} + 2 q^{13} - 4 q^{14} - q^{16} - 2 q^{17} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

sage: E.isogeny_class().matrix()
 

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.