Properties

Label 88305.k
Number of curves 4
Conductor 88305
CM no
Rank 1
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("88305.k1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 88305.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
88305.k1 88305k4 [1, 1, 1, -94630, -11243098] [2] 401408  
88305.k2 88305k2 [1, 1, 1, -6325, -151990] [2, 2] 200704  
88305.k3 88305k1 [1, 1, 1, -2120, 34712] [2] 100352 \(\Gamma_0(N)\)-optimal
88305.k4 88305k3 [1, 1, 1, 14700, -925710] [2] 401408  

Rank

sage: E.rank()
 

The elliptic curves in class 88305.k have rank \(1\).

Modular form 88305.2.a.k

sage: E.q_eigenform(10)
 
\( q - q^{2} - q^{3} - q^{4} + q^{5} + q^{6} + q^{7} + 3q^{8} + q^{9} - q^{10} + q^{12} - 6q^{13} - q^{14} - q^{15} - q^{16} - 2q^{17} - q^{18} + 8q^{19} + O(q^{20}) \)

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.