Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("242550.md1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 242550.md

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
242550.md1 242550md4 [1, -1, 1, -287929130, -1827155344003] [2] 95551488  
242550.md2 242550md2 [1, -1, 1, -39425630, 94446589997] [2] 31850496  
242550.md3 242550md1 [1, -1, 1, -617630, 3635869997] [2] 15925248 \(\Gamma_0(N)\)-optimal
242550.md4 242550md3 [1, -1, 1, 5556370, -97938778003] [2] 47775744  

Rank

sage: E.rank()
 

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

Modular form 242550.2.a.md

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

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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.