Properties

Label 381150.gy
Number of curves $4$
Conductor $381150$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("381150.gy1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 381150.gy

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
381150.gy1 381150gy3 [1, -1, 0, -1271067, 483642341] [2] 9953280  
381150.gy2 381150gy1 [1, -1, 0, -318192, -68919284] [2] 3317760 \(\Gamma_0(N)\)-optimal
381150.gy3 381150gy2 [1, -1, 0, -227442, -109121534] [2] 6635520  
381150.gy4 381150gy4 [1, -1, 0, 1995933, 2558187341] [2] 19906560  

Rank

sage: E.rank()
 

The elliptic curves in class 381150.gy have rank \(1\).

Modular form 381150.2.a.gy

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

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.

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.