Properties

Label 308550jf
Number of curves 6
Conductor 308550
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("308550.jf1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 308550jf

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
308550.jf4 308550jf1 [1, 0, 0, -22112813, -40025182383] [2] 17694720 \(\Gamma_0(N)\)-optimal
308550.jf3 308550jf2 [1, 0, 0, -22354813, -39104372383] [2, 2] 35389440  
308550.jf2 308550jf3 [1, 0, 0, -60167313, 128064690117] [2, 2] 70778880  
308550.jf5 308550jf4 [1, 0, 0, 11585687, -147340626883] [2] 70778880  
308550.jf1 308550jf5 [1, 0, 0, -883723563, 10110389996367] [2] 141557760  
308550.jf6 308550jf6 [1, 0, 0, 158388937, 844710633867] [2] 141557760  

Rank

sage: E.rank()
 

The elliptic curves in class 308550jf have rank \(1\).

Modular form 308550.2.a.jf

sage: E.q_eigenform(10)
 
\( q + q^{2} + q^{3} + q^{4} + q^{6} + q^{8} + q^{9} + q^{12} + 6q^{13} + q^{16} + q^{17} + q^{18} - 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 2 & 2 \\ 4 & 2 & 4 & 1 & 8 & 8 \\ 8 & 4 & 2 & 8 & 1 & 4 \\ 8 & 4 & 2 & 8 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.