Properties

Label 126350.dh
Number of curves $4$
Conductor $126350$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("126350.dh1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 126350.dh

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
126350.dh1 126350cu4 [1, -1, 1, -2415880, 1445843497] [2] 2764800  
126350.dh2 126350cu3 [1, -1, 1, -791380, -253022503] [2] 2764800  
126350.dh3 126350cu2 [1, -1, 1, -159630, 19893497] [2, 2] 1382400  
126350.dh4 126350cu1 [1, -1, 1, 20870, 1843497] [2] 691200 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 126350.dh have rank \(0\).

Modular form 126350.2.a.dh

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.