Properties

Label 395798.o
Number of curves 3
Conductor 395798
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("395798.o1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 395798.o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
395798.o1 395798o3 [1, 0, 0, -641366918, -6492323742620] [] 168521472  
395798.o2 395798o1 [1, 0, 0, -6016488, 6413883904] [] 18724608 \(\Gamma_0(N)\)-optimal
395798.o3 395798o2 [1, 0, 0, 40395137, -23819391207] [] 56173824  

Rank

sage: E.rank()
 

The elliptic curves in class 395798.o have rank \(1\).

Modular form 395798.2.a.o

sage: E.q_eigenform(10)
 
\( q + q^{2} - 2q^{3} + q^{4} - 2q^{6} + q^{7} + q^{8} + q^{9} - 3q^{11} - 2q^{12} + q^{14} + q^{16} - 3q^{17} + q^{18} - 2q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.