Properties

Label 58080.bw
Number of curves $4$
Conductor $58080$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("bw1")
 
E.isogeny_class()
 

Elliptic curves in class 58080.bw

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
58080.bw1 58080x4 \([0, 1, 0, -19400, -1046520]\) \(890277128/15\) \(13605588480\) \([2]\) \(92160\) \(1.0748\)  
58080.bw2 58080x3 \([0, 1, 0, -4880, 113628]\) \(14172488/1875\) \(1700698560000\) \([2]\) \(92160\) \(1.0748\)  
58080.bw3 58080x1 \([0, 1, 0, -1250, -15600]\) \(1906624/225\) \(25510478400\) \([2, 2]\) \(46080\) \(0.72818\) \(\Gamma_0(N)\)-optimal
58080.bw4 58080x2 \([0, 1, 0, 1775, -76705]\) \(85184/405\) \(-2938807111680\) \([2]\) \(92160\) \(1.0748\)  

Rank

sage: E.rank()
 

The elliptic curves in class 58080.bw have rank \(0\).

Complex multiplication

The elliptic curves in class 58080.bw do not have complex multiplication.

Modular form 58080.2.a.bw

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{5} + q^{9} - 2 q^{13} + q^{15} - 6 q^{17} - 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.