Properties

Label 242550.nq
Number of curves 4
Conductor 242550
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("242550.nq1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 242550.nq

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
242550.nq1 242550nq3 [1, -1, 1, -363726005, 2670048155247] [2] 56623104  
242550.nq2 242550nq2 [1, -1, 1, -23384255, 39206427747] [2, 2] 28311552  
242550.nq3 242550nq1 [1, -1, 1, -5523755, -4337471253] [2] 14155776 \(\Gamma_0(N)\)-optimal
242550.nq4 242550nq4 [1, -1, 1, 31189495, 194959910247] [2] 56623104  

Rank

sage: E.rank()
 

The elliptic curves in class 242550.nq have rank \(1\).

Modular form 242550.2.a.nq

sage: E.q_eigenform(10)
 
\( q + q^{2} + q^{4} + q^{8} + q^{11} + 2q^{13} + q^{16} - 2q^{17} - 4q^{19} + O(q^{20}) \)

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 LMFDB 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 LMFDB labels.