Properties

Label 162450dq
Number of curves $4$
Conductor $162450$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("162450.w1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 162450dq

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
162450.w3 162450dq1 [1, -1, 0, -2519667, 1530856741] [2] 4423680 \(\Gamma_0(N)\)-optimal
162450.w2 162450dq2 [1, -1, 0, -4144167, -683336759] [2, 2] 8847360  
162450.w4 162450dq3 [1, -1, 0, 16162083, -5414693009] [2] 17694720  
162450.w1 162450dq4 [1, -1, 0, -50442417, -137679858509] [2] 17694720  

Rank

sage: E.rank()
 

The elliptic curves in class 162450dq have rank \(1\).

Modular form 162450.2.a.w

sage: E.q_eigenform(10)
 
\( q - q^{2} + q^{4} - q^{8} - 4q^{11} + 2q^{13} + q^{16} + 2q^{17} + O(q^{20}) \)

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.