Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("162450.d1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 162450dd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
162450.d4 162450dd1 [1, -1, 0, -813942, 482503716] [2] 6635520 \(\Gamma_0(N)\)-optimal
162450.d3 162450dd2 [1, -1, 0, -15434442, 23334345216] [2, 2] 13271040  
162450.d1 162450dd3 [1, -1, 0, -246925692, 1493535273966] [2] 26542080  
162450.d2 162450dd4 [1, -1, 0, -17871192, 15475826466] [2] 26542080  

Rank

sage: E.rank()
 

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

Modular form 162450.2.a.d

sage: E.q_eigenform(10)
 
\( q - q^{2} + q^{4} - 4q^{7} - q^{8} + 4q^{11} - 2q^{13} + 4q^{14} + q^{16} - 2q^{17} + O(q^{20}) \)

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.