Properties

Label 89280.dm
Number of curves $2$
Conductor $89280$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("dm1")
 
E.isogeny_class()
 

Elliptic curves in class 89280.dm

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
89280.dm1 89280ch2 \([0, 0, 0, -1159212, 168321584]\) \(901456690969801/457629750000\) \(87454407131136000000\) \([2]\) \(2949120\) \(2.5189\)  
89280.dm2 89280ch1 \([0, 0, 0, 269268, 20331056]\) \(11298232190519/7472736000\) \(-1428062088462336000\) \([2]\) \(1474560\) \(2.1724\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 89280.dm have rank \(1\).

Complex multiplication

The elliptic curves in class 89280.dm do not have complex multiplication.

Modular form 89280.2.a.dm

sage: E.q_eigenform(10)
 
\(q + q^{5} - 2 q^{7} - 4 q^{11} + 4 q^{13} - 2 q^{17} + 8 q^{19} + O(q^{20})\) 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 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.