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Properties

Label 1089h
Number of curves $2$
Conductor $1089$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("h1")
 
E.isogeny_class()
 

Elliptic curves in class 1089h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1089.c2 1089h1 \([1, -1, 1, -23, 168]\) \(-121\) \(-10673289\) \([]\) \(144\) \(0.031345\) \(\Gamma_0(N)\)-optimal
1089.c1 1089h2 \([1, -1, 1, -32693, -2267130]\) \(-24729001\) \(-156267624249\) \([]\) \(1584\) \(1.2303\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 1089.2.a.h

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

\(\left(\begin{array}{rr} 1 & 11 \\ 11 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.