Properties

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

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Show commands: SageMath
E = EllipticCurve("f1")
 
E.isogeny_class()
 

Elliptic curves in class 1089f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1089.i2 1089f1 \([1, -1, 0, -270, 1777]\) \(-24729001\) \(-88209\) \([]\) \(144\) \(0.031345\) \(\Gamma_0(N)\)-optimal
1089.i1 1089f2 \([1, -1, 0, -2745, -215726]\) \(-121\) \(-18908382534129\) \([]\) \(1584\) \(1.2303\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 1089.2.a.f

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.