Properties

Label 127050.hx
Number of curves 4
Conductor 127050
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("127050.hx1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 127050.hx

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
127050.hx1 127050hg4 [1, 0, 0, -99797838, -383737186458] [2] 17694720  
127050.hx2 127050hg2 [1, 0, 0, -6416088, -5634480708] [2, 2] 8847360  
127050.hx3 127050hg1 [1, 0, 0, -1515588, 623457792] [4] 4423680 \(\Gamma_0(N)\)-optimal
127050.hx4 127050hg3 [1, 0, 0, 8557662, -28020236958] [2] 17694720  

Rank

sage: E.rank()
 

The elliptic curves in class 127050.hx have rank \(0\).

Modular form 127050.2.a.hx

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.