Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("265200.ba1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 265200.ba

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
265200.ba1 265200ba1 [0, -1, 0, -5448008, -4836841488] [2] 8847360 \(\Gamma_0(N)\)-optimal
265200.ba2 265200ba2 [0, -1, 0, -840008, -12762601488] [2] 17694720  

Rank

sage: E.rank()
 

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

Modular form 265200.2.a.ba

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.