Properties

Label 265200u
Number of curves 2
Conductor 265200
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("265200.u1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 265200u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
265200.u1 265200u1 [0, -1, 0, -77229883, 261255393262] [2] 24330240 \(\Gamma_0(N)\)-optimal
265200.u2 265200u2 [0, -1, 0, -75387508, 274310462512] [2] 48660480  

Rank

sage: E.rank()
 

The elliptic curves in class 265200u have rank \(0\).

Modular form 265200.2.a.u

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

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.