Properties

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

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

Elliptic curves in class 265200r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
265200.r1 265200r1 \([0, -1, 0, -2442508, 1426112512]\) \(402876451435348816/13746755117745\) \(54987020470980000000\) \([2]\) \(8847360\) \(2.5598\) \(\Gamma_0(N)\)-optimal
265200.r2 265200r2 \([0, -1, 0, 837992, 4969052512]\) \(4067455675907516/669098843633025\) \(-10705581498128400000000\) \([2]\) \(17694720\) \(2.9064\)  

Rank

sage: E.rank()
 

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

Complex multiplication

The elliptic curves in class 265200r do not have complex multiplication.

Modular form 265200.2.a.r

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

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.