Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("cx1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 87120.cx

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
87120.cx1 87120bi4 \([0, 0, 0, -11500203, 15010887562]\) \(127191074376964/495\) \(654619284126720\) \([2]\) \(1966080\) \(2.4791\)  
87120.cx2 87120bi2 \([0, 0, 0, -719103, 234311902]\) \(124386546256/245025\) \(81009136410681600\) \([2, 2]\) \(983040\) \(2.1325\)  
87120.cx3 87120bi3 \([0, 0, 0, -479523, 392961778]\) \(-9220796644/45106875\) \(-59652182266047360000\) \([2]\) \(1966080\) \(2.4791\)  
87120.cx4 87120bi1 \([0, 0, 0, -60258, 949003]\) \(1171019776/658845\) \(13614035424572880\) \([2]\) \(491520\) \(1.7859\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 87120.2.a.cx

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

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.