Properties

Label 1089.h
Number of curves $2$
Conductor $1089$
CM no
Rank $0$
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Show commands: SageMath
sage: E = EllipticCurve("h1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1089.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1089.h1 1089c2 \([1, -1, 0, -2019, -34226]\) \(19034163/121\) \(5787689787\) \([2]\) \(960\) \(0.71026\)  
1089.h2 1089c1 \([1, -1, 0, -204, 259]\) \(19683/11\) \(526153617\) \([2]\) \(480\) \(0.36368\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 1089.h have rank \(0\).

Complex multiplication

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

Modular form 1089.2.a.h

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{4} - 4q^{5} + 2q^{7} - 3q^{8} - 4q^{10} + 2q^{13} + 2q^{14} - q^{16} - 2q^{17} + 6q^{19} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.