Properties

Label 99450co
Number of curves 4
Conductor 99450
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("99450.ce1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 99450co

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
99450.ce4 99450co1 [1, -1, 1, 355495, -13922503] [2] 2211840 \(\Gamma_0(N)\)-optimal
99450.ce3 99450co2 [1, -1, 1, -1444505, -111122503] [2, 2] 4423680  
99450.ce2 99450co3 [1, -1, 1, -14449505, 21035007497] [2] 8847360  
99450.ce1 99450co4 [1, -1, 1, -17239505, -27499652503] [2] 8847360  

Rank

sage: E.rank()
 

The elliptic curves in class 99450co have rank \(1\).

Modular form 99450.2.a.ce

sage: E.q_eigenform(10)
 
\( q + q^{2} + q^{4} - 4q^{7} + q^{8} + 4q^{11} - q^{13} - 4q^{14} + q^{16} - q^{17} + 8q^{19} + O(q^{20}) \)

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 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.