Properties

Label 124950.cp
Number of curves 6
Conductor 124950
CM no
Rank 2
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("124950.cp1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 124950.cp

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
124950.cp1 124950de6 [1, 0, 1, -33986426, 76258844498] [2] 6291456  
124950.cp2 124950de4 [1, 0, 1, -2124176, 1191383498] [2, 2] 3145728  
124950.cp3 124950de5 [1, 0, 1, -2013926, 1320596498] [2] 6291456  
124950.cp4 124950de2 [1, 0, 1, -139676, 16559498] [2, 2] 1572864  
124950.cp5 124950de1 [1, 0, 1, -41676, -3040502] [2] 786432 \(\Gamma_0(N)\)-optimal
124950.cp6 124950de3 [1, 0, 1, 276824, 96527498] [2] 3145728  

Rank

sage: E.rank()
 

The elliptic curves in class 124950.cp have rank \(2\).

Modular form 124950.2.a.cp

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.