Properties

Label 102550.q
Number of curves 2
Conductor 102550
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("102550.q1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 102550.q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
102550.q1 102550g2 [1, -1, 0, -138649042, -628720244134] [] 66382848  
102550.q2 102550g1 [1, -1, 0, 239708, 291889616] [] 9483264 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 102550.q have rank \(0\).

Modular form 102550.2.a.q

sage: E.q_eigenform(10)
 
\( q - q^{2} + 3q^{3} + q^{4} - 3q^{6} - q^{7} - q^{8} + 6q^{9} + 5q^{11} + 3q^{12} - 7q^{13} + q^{14} + q^{16} + 3q^{17} - 6q^{18} - 8q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.