Properties

Label 87120.ci
Number of curves $4$
Conductor $87120$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

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

Elliptic curves in class 87120.ci

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
87120.ci1 87120cy4 \([0, 0, 0, -421443, -27527742]\) \(57960603/31250\) \(4463313300864000000\) \([2]\) \(1244160\) \(2.2696\)  
87120.ci2 87120cy2 \([0, 0, 0, -247203, 47306402]\) \(8527173507/200\) \(39184094822400\) \([2]\) \(414720\) \(1.7203\)  
87120.ci3 87120cy1 \([0, 0, 0, -14883, 795938]\) \(-1860867/320\) \(-62694551715840\) \([2]\) \(207360\) \(1.3737\) \(\Gamma_0(N)\)-optimal
87120.ci4 87120cy3 \([0, 0, 0, 101277, -3378078]\) \(804357/500\) \(-71413012813824000\) \([2]\) \(622080\) \(1.9230\)  

Rank

sage: E.rank()
 

The elliptic curves in class 87120.ci have rank \(1\).

Complex multiplication

The elliptic curves in class 87120.ci do not have complex multiplication.

Modular form 87120.2.a.ci

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

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.