Properties

Label 88935.j
Number of curves 4
Conductor 88935
CM no
Rank 1
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("88935.j1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 88935.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
88935.j1 88935p4 [1, 1, 1, -667136, -209997292] [2] 1105920  
88935.j2 88935p2 [1, 1, 1, -44591, -2814316] [2, 2] 552960  
88935.j3 88935p1 [1, 1, 1, -14946, 660078] [2] 276480 \(\Gamma_0(N)\)-optimal
88935.j4 88935p3 [1, 1, 1, 103634, -17399656] [2] 1105920  

Rank

sage: E.rank()
 

The elliptic curves in class 88935.j have rank \(1\).

Modular form 88935.2.a.j

sage: E.q_eigenform(10)
 
\( q - q^{2} - q^{3} - q^{4} - q^{5} + q^{6} + 3q^{8} + q^{9} + q^{10} + q^{12} - 6q^{13} + q^{15} - q^{16} + 2q^{17} - q^{18} - 8q^{19} + O(q^{20}) \)

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 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.