↑

Properties

Label 266805.ea
Number of curves $2$
Conductor $266805$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("ea1")
 
E.isogeny_class()
 

Elliptic curves in class 266805.ea

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
266805.ea1 266805ea2 \([1, -1, 0, -20169, -783700]\) \(55306341/15625\) \(256350412828125\) \([2]\) \(1075200\) \(1.4717\)  
266805.ea2 266805ea1 \([1, -1, 0, -7464, 240323]\) \(2803221/125\) \(2050803302625\) \([2]\) \(537600\) \(1.1251\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 266805.ea have rank \(0\).

Complex multiplication

The elliptic curves in class 266805.ea do not have complex multiplication.

Modular form 266805.2.a.ea

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{4} + q^{5} - 3 q^{8} + q^{10} + 6 q^{13} - q^{16} + 6 q^{17} - 6 q^{19} + O(q^{20})\) 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 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.