Properties

Label 73920.cw
Number of curves $4$
Conductor $73920$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("cw1")
 
E.isogeny_class()
 

Elliptic curves in class 73920.cw

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
73920.cw1 73920bg4 \([0, -1, 0, -19745, -1061343]\) \(12990838708516/144375\) \(9461760000\) \([2]\) \(98304\) \(1.0677\)  
73920.cw2 73920bg2 \([0, -1, 0, -1265, -15375]\) \(13674725584/1334025\) \(21856665600\) \([2, 2]\) \(49152\) \(0.72109\)  
73920.cw3 73920bg1 \([0, -1, 0, -285, 1677]\) \(2508888064/396165\) \(405672960\) \([2]\) \(24576\) \(0.37452\) \(\Gamma_0(N)\)-optimal
73920.cw4 73920bg3 \([0, -1, 0, 1535, -76415]\) \(6099383804/41507235\) \(-2720218152960\) \([2]\) \(98304\) \(1.0677\)  

Rank

sage: E.rank()
 

The elliptic curves in class 73920.cw have rank \(1\).

Complex multiplication

The elliptic curves in class 73920.cw do not have complex multiplication.

Modular form 73920.2.a.cw

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{5} - q^{7} + q^{9} + q^{11} - 2 q^{13} - q^{15} + 6 q^{17} + O(q^{20})\) 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.