Properties

Label 99450.de
Number of curves 2
Conductor 99450
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("99450.de1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 99450.de

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
99450.de1 99450cw1 [1, -1, 1, -3064505, -2040542503] [2] 2949120 \(\Gamma_0(N)\)-optimal
99450.de2 99450cw2 [1, -1, 1, -472505, -5384222503] [2] 5898240  

Rank

sage: E.rank()
 

The elliptic curves in class 99450.de have rank \(0\).

Modular form 99450.2.a.de

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.