# Properties

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

# Related objects

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)

$$q - q^{5} + 2q^{7} + 4q^{13} - 6q^{17} - 4q^{19} + O(q^{20})$$

## 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.