Properties

Label 91200ed
Number of curves $4$
Conductor $91200$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("91200.ff1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 91200ed

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
91200.ff4 91200ed1 [0, 1, 0, -16033, 1328063] [2] 442368 \(\Gamma_0(N)\)-optimal
91200.ff3 91200ed2 [0, 1, 0, -304033, 64400063] [2, 2] 884736  
91200.ff2 91200ed3 [0, 1, 0, -352033, 42656063] [2] 1769472  
91200.ff1 91200ed4 [0, 1, 0, -4864033, 4127360063] [2] 1769472  

Rank

sage: E.rank()
 

The elliptic curves in class 91200ed have rank \(1\).

Modular form 91200.2.a.ff

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 Cremona 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 Cremona labels.