Properties

Label 381150pk
Number of curves $4$
Conductor $381150$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("381150.pk1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 381150pk

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
381150.pk3 381150pk1 [1, -1, 1, -141230, -17865603] [2] 3317760 \(\Gamma_0(N)\)-optimal
381150.pk4 381150pk2 [1, -1, 1, 221770, -94821603] [2] 6635520  
381150.pk1 381150pk3 [1, -1, 1, -2863730, 1863684397] [2] 9953280  
381150.pk2 381150pk4 [1, -1, 1, -2046980, 2948328397] [2] 19906560  

Rank

sage: E.rank()
 

The elliptic curves in class 381150pk have rank \(0\).

Modular form 381150.2.a.pk

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 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.