Properties

Label 236691.o
Number of curves $2$
Conductor $236691$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("o1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 236691.o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
236691.o1 236691o1 \([1, -1, 0, -1183509, -495012056]\) \(10418796526321/6390657\) \(112451839809475257\) \([2]\) \(5160960\) \(2.2146\) \(\Gamma_0(N)\)-optimal
236691.o2 236691o2 \([1, -1, 0, -962424, -685808411]\) \(-5602762882081/8312741073\) \(-146273384335701550473\) \([2]\) \(10321920\) \(2.5611\)  

Rank

sage: E.rank()
 

The elliptic curves in class 236691.o have rank \(1\).

Complex multiplication

The elliptic curves in class 236691.o do not have complex multiplication.

Modular form 236691.2.a.o

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{4} - 4q^{5} - q^{7} - 3q^{8} - 4q^{10} - 4q^{11} + q^{13} - q^{14} - q^{16} + O(q^{20})\)  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 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.