Properties

Label 91200.cf
Number of curves $4$
Conductor $91200$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("91200.cf1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 91200.cf

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
91200.cf1 91200x4 [0, -1, 0, -993633, -380344863] [2] 1179648  
91200.cf2 91200x2 [0, -1, 0, -81633, -1864863] [2, 2] 589824  
91200.cf3 91200x1 [0, -1, 0, -49633, 4247137] [2] 294912 \(\Gamma_0(N)\)-optimal
91200.cf4 91200x3 [0, -1, 0, 318367, -15064863] [2] 1179648  

Rank

sage: E.rank()
 

The elliptic curves in class 91200.cf have rank \(0\).

Modular form 91200.2.a.cf

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.