# Properties

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

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 $$[0, 0, 0, -11500203, 15010887562]$$ $$127191074376964/495$$ $$654619284126720$$ $$$$ $$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$$ $$$$ $$1966080$$ $$2.4791$$
87120.cx4 87120bi1 $$[0, 0, 0, -60258, 949003]$$ $$1171019776/658845$$ $$13614035424572880$$ $$$$ $$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)

$$q - q^{5} + 4q^{7} - 2q^{13} - 2q^{17} + 4q^{19} + O(q^{20})$$ ## 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. 