Properties

Label 331200.jf
Number of curves $6$
Conductor $331200$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("331200.jf1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 331200.jf

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
331200.jf1 331200jf4 [0, 0, 0, -1589760300, -24397514498000] [2] 56623104  
331200.jf2 331200jf5 [0, 0, 0, -371952300, 2365109278000] [2] 113246208  
331200.jf3 331200jf3 [0, 0, 0, -101952300, -360270722000] [2, 2] 56623104  
331200.jf4 331200jf2 [0, 0, 0, -99360300, -381208898000] [2, 2] 28311552  
331200.jf5 331200jf1 [0, 0, 0, -6048300, -6281282000] [2] 14155776 \(\Gamma_0(N)\)-optimal
331200.jf6 331200jf6 [0, 0, 0, 126575700, -1745607458000] [2] 113246208  

Rank

sage: E.rank()
 

The elliptic curves in class 331200.jf have rank \(0\).

Modular form 331200.2.a.jf

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

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.