↑

Properties

Label 259182.eo
Number of curves $2$
Conductor $259182$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("eo1")
 
E.isogeny_class()
 

Elliptic curves in class 259182.eo

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
259182.eo1 259182eo1 \([1, -1, 1, -485, -4111]\) \(-3854428875/137564\) \(-449421588\) \([]\) \(117504\) \(0.43238\) \(\Gamma_0(N)\)-optimal
259182.eo2 259182eo2 \([1, -1, 1, 2320, -14957]\) \(580078125/373184\) \(-888791061312\) \([]\) \(352512\) \(0.98169\)  

Rank

sage: E.rank()
 

The elliptic curves in class 259182.eo have rank \(1\).

Complex multiplication

The elliptic curves in class 259182.eo do not have complex multiplication.

Modular form 259182.2.a.eo

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} - q^{7} + q^{8} + 4 q^{13} - q^{14} + q^{16} - q^{17} - 5 q^{19} + O(q^{20})\) 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 LMFDB numbering.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.