Properties

Label 265200.r
Number of curves 2
Conductor 265200
CM no
Rank 1
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("265200.r1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 265200.r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
265200.r1 265200r1 [0, -1, 0, -2442508, 1426112512] [2] 8847360 \(\Gamma_0(N)\)-optimal
265200.r2 265200r2 [0, -1, 0, 837992, 4969052512] [2] 17694720  

Rank

sage: E.rank()
 

The elliptic curves in class 265200.r have rank \(1\).

Modular form 265200.2.a.r

sage: E.q_eigenform(10)
 
\( q - q^{3} - 2q^{7} + q^{9} - 4q^{11} - q^{13} - q^{17} - 6q^{19} + O(q^{20}) \)

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.