Properties

Label 54720ec
Number of curves $2$
Conductor $54720$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("ec1")
 
E.isogeny_class()
 

Elliptic curves in class 54720ec

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
54720.v2 54720ec1 \([0, 0, 0, -838668, -296976368]\) \(-341370886042369/1817528220\) \(-347335051805982720\) \([2]\) \(860160\) \(2.2105\) \(\Gamma_0(N)\)-optimal
54720.v1 54720ec2 \([0, 0, 0, -13435788, -18955830512]\) \(1403607530712116449/39475350\) \(7543856863641600\) \([2]\) \(1720320\) \(2.5571\)  

Rank

sage: E.rank()
 

The elliptic curves in class 54720ec have rank \(0\).

Complex multiplication

The elliptic curves in class 54720ec do not have complex multiplication.

Modular form 54720.2.a.ec

sage: E.q_eigenform(10)
 
\(q - q^{5} - 2 q^{7} + 4 q^{11} - 6 q^{13} - 4 q^{17} + q^{19} + O(q^{20})\) 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.