Properties

Label 122694bd
Number of curves 4
Conductor 122694
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("122694.bj1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 122694bd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
122694.bj3 122694bd1 [1, 0, 1, -112896, -13780934] [2] 1036800 \(\Gamma_0(N)\)-optimal
122694.bj4 122694bd2 [1, 0, 1, 91594, -58114366] [2] 2073600  
122694.bj1 122694bd3 [1, 0, 1, -1646571, 809986582] [2] 3110400  
122694.bj2 122694bd4 [1, 0, 1, -828611, 1615186406] [2] 6220800  

Rank

sage: E.rank()
 

The elliptic curves in class 122694bd have rank \(1\).

Modular form 122694.2.a.bj

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

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.