Properties

Label 262080f
Number of curves 2
Conductor 262080
CM no
Rank 2
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("262080.f1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 262080f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
262080.f2 262080f1 [0, 0, 0, -20088, 6481512] [2] 2162688 \(\Gamma_0(N)\)-optimal
262080.f1 262080f2 [0, 0, 0, -658908, 205026768] [2] 4325376  

Rank

sage: E.rank()
 

The elliptic curves in class 262080f have rank \(2\).

Modular form 262080.2.a.f

sage: E.q_eigenform(10)
 
\( q - q^{5} - q^{7} - 6q^{11} + q^{13} - 2q^{17} - 4q^{19} + O(q^{20}) \)

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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.