Properties

Label 270480.fj
Number of curves $6$
Conductor $270480$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("270480.fj1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 270480.fj

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
270480.fj1 270480fj3 [0, 1, 0, -86553616, 309909944084] [2] 14155776  
270480.fj2 270480fj6 [0, 1, 0, -20250736, -30052397740] [2] 28311552  
270480.fj3 270480fj4 [0, 1, 0, -5550736, 4574922260] [2, 2] 14155776  
270480.fj4 270480fj2 [0, 1, 0, -5409616, 4840961684] [2, 2] 7077888  
270480.fj5 270480fj1 [0, 1, 0, -329296, 79685780] [2] 3538944 \(\Gamma_0(N)\)-optimal
270480.fj6 270480fj5 [0, 1, 0, 6891344, 22177977044] [2] 28311552  

Rank

sage: E.rank()
 

The elliptic curves in class 270480.fj have rank \(1\).

Modular form 270480.2.a.fj

sage: E.q_eigenform(10)
 
\( q + q^{3} - q^{5} + q^{9} - 4q^{11} + 2q^{13} - q^{15} + 6q^{17} + 4q^{19} + O(q^{20}) \)

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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.