Properties

Label 88725s
Number of curves 4
Conductor 88725
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("88725.cb1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 88725s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
88725.cb3 88725s1 [1, 1, 0, -10650, 396375] [2] 184320 \(\Gamma_0(N)\)-optimal
88725.cb2 88725s2 [1, 1, 0, -31775, -1695000] [2, 2] 368640  
88725.cb4 88725s3 [1, 1, 0, 73850, -10461875] [2] 737280  
88725.cb1 88725s4 [1, 1, 0, -475400, -126353625] [2] 737280  

Rank

sage: E.rank()
 

The elliptic curves in class 88725s have rank \(0\).

Modular form 88725.2.a.cb

sage: E.q_eigenform(10)
 
\( q + q^{2} - q^{3} - q^{4} - q^{6} + q^{7} - 3q^{8} + q^{9} + q^{12} + q^{14} - q^{16} - 2q^{17} + q^{18} + 8q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.