Properties

Label 10944.o
Number of curves $4$
Conductor $10944$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("o1")
 
E.isogeny_class()
 

Elliptic curves in class 10944.o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
10944.o1 10944bh3 \([0, 0, 0, -58476, -5442640]\) \(115714886617/1539\) \(294107480064\) \([2]\) \(24576\) \(1.3440\)  
10944.o2 10944bh2 \([0, 0, 0, -3756, -80080]\) \(30664297/3249\) \(620893569024\) \([2, 2]\) \(12288\) \(0.99745\)  
10944.o3 10944bh1 \([0, 0, 0, -876, 8624]\) \(389017/57\) \(10892869632\) \([2]\) \(6144\) \(0.65087\) \(\Gamma_0(N)\)-optimal
10944.o4 10944bh4 \([0, 0, 0, 4884, -394576]\) \(67419143/390963\) \(-74714192805888\) \([2]\) \(24576\) \(1.3440\)  

Rank

sage: E.rank()
 

The elliptic curves in class 10944.o have rank \(1\).

Complex multiplication

The elliptic curves in class 10944.o do not have complex multiplication.

Modular form 10944.2.a.o

sage: E.q_eigenform(10)
 
\(q - 2 q^{5} - 6 q^{13} + 6 q^{17} + q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.