Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("91200.ef1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 91200.ef

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
91200.ef1 91200fm4 [0, -1, 0, -4864033, -4127360063] [2] 1769472  
91200.ef2 91200fm3 [0, -1, 0, -352033, -42656063] [2] 1769472  
91200.ef3 91200fm2 [0, -1, 0, -304033, -64400063] [2, 2] 884736  
91200.ef4 91200fm1 [0, -1, 0, -16033, -1328063] [2] 442368 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Modular form 91200.2.a.ef

sage: E.q_eigenform(10)
 
\( q - q^{3} + 4q^{7} + q^{9} - 4q^{11} - 2q^{13} + 2q^{17} - q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.