Properties

Label 381150ev
Number of curves 4
Conductor 381150
CM no
Rank 2
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("381150.ev1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 381150ev

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
381150.ev3 381150ev1 [1, -1, 0, -1525167, 14108653741] [2] 39813120 \(\Gamma_0(N)\)-optimal
381150.ev2 381150ev2 [1, -1, 0, -97357167, 366482917741] [2] 79626240  
381150.ev4 381150ev3 [1, -1, 0, 13720833, -380046184259] [2] 119439360  
381150.ev1 381150ev4 [1, -1, 0, -711008667, -7090316624759] [2] 238878720  

Rank

sage: E.rank()
 

The elliptic curves in class 381150ev have rank \(2\).

Modular form 381150.2.a.ev

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

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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.