Properties

Label 124950.cb
Number of curves $6$
Conductor $124950$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("124950.cb1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 124950.cb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
124950.cb1 124950ba6 [1, 1, 0, -16805289925, 838520099849125] [2] 188743680  
124950.cb2 124950ba4 [1, 1, 0, -1052328925, 13049190488125] [2, 2] 94371840  
124950.cb3 124950ba5 [1, 1, 0, -358439925, 30001592647125] [2] 188743680  
124950.cb4 124950ba2 [1, 1, 0, -111136925, -113379631875] [2, 2] 47185920  
124950.cb5 124950ba1 [1, 1, 0, -86048925, -306883375875] [2] 23592960 \(\Gamma_0(N)\)-optimal
124950.cb6 124950ba3 [1, 1, 0, 428647075, -891208375875] [2] 94371840  

Rank

sage: E.rank()
 

The elliptic curves in class 124950.cb have rank \(1\).

Modular form 124950.2.a.cb

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

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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.