Properties

Label 381150db
Number of curves 4
Conductor 381150
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("381150.db1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 381150db

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
381150.db3 381150db1 [1, -1, 0, -13640292, -16833360384] [2] 35389440 \(\Gamma_0(N)\)-optimal
381150.db2 381150db2 [1, -1, 0, -57744792, 152130979116] [2, 2] 70778880  
381150.db1 381150db3 [1, -1, 0, -898180542, 10360904034366] [2] 141557760  
381150.db4 381150db4 [1, -1, 0, 77018958, 756546397866] [2] 141557760  

Rank

sage: E.rank()
 

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

Modular form 381150.2.a.db

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

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.