Properties

Label 69938e
Number of curves 4
Conductor 69938
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("69938.f1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 69938e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
69938.f4 69938e1 [1, 1, 0, -105635, -8225587] [2] 622080 \(\Gamma_0(N)\)-optimal
69938.f3 69938e2 [1, 1, 0, -1504395, -710682859] [2] 1244160  
69938.f2 69938e3 [1, 1, 0, -3602535, 2629975649] [2] 1866240  
69938.f1 69938e4 [1, 1, 0, -3952225, 2088165963] [2] 3732480  

Rank

sage: E.rank()
 

The elliptic curves in class 69938e have rank \(0\).

Modular form 69938.2.a.f

sage: E.q_eigenform(10)
 
\( q - q^{2} + 2q^{3} + q^{4} - 2q^{6} - 4q^{7} - q^{8} + q^{9} + 2q^{12} - 2q^{13} + 4q^{14} + q^{16} - q^{18} + 4q^{19} + O(q^{20}) \)

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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.