Properties

Label 18240.ci
Number of curves $2$
Conductor $18240$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("ci1")
 
E.isogeny_class()
 

Elliptic curves in class 18240.ci

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
18240.ci1 18240cx2 \([0, 1, 0, -1492865, 701570175]\) \(1403607530712116449/39475350\) \(10348226150400\) \([2]\) \(215040\) \(2.0078\)  
18240.ci2 18240cx1 \([0, 1, 0, -93185, 10968063]\) \(-341370886042369/1817528220\) \(-476454117703680\) \([2]\) \(107520\) \(1.6612\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 18240.ci have rank \(1\).

Complex multiplication

The elliptic curves in class 18240.ci do not have complex multiplication.

Modular form 18240.2.a.ci

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{5} - 2 q^{7} + q^{9} - 4 q^{11} - 6 q^{13} + q^{15} + 4 q^{17} + q^{19} + O(q^{20})\) 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 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.