Properties

Label 55440co
Number of curves $2$
Conductor $55440$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("co1")
 
E.isogeny_class()
 

Elliptic curves in class 55440co

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
55440.ew1 55440co1 \([0, 0, 0, -33507, 2182626]\) \(51603494067/4336640\) \(349626716651520\) \([2]\) \(184320\) \(1.5324\) \(\Gamma_0(N)\)-optimal
55440.ew2 55440co2 \([0, 0, 0, 35613, 10020834]\) \(61958108493/573927200\) \(-46270910781849600\) \([2]\) \(368640\) \(1.8790\)  

Rank

sage: E.rank()
 

The elliptic curves in class 55440co have rank \(1\).

Complex multiplication

The elliptic curves in class 55440co do not have complex multiplication.

Modular form 55440.2.a.co

sage: E.q_eigenform(10)
 
\(q + q^{5} + q^{7} + q^{11} + 2 q^{13} + 2 q^{19} + O(q^{20})\) 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.