# Properties

 Label 87120.ds Number of curves $2$ Conductor $87120$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("ds1")

sage: E.isogeny_class()

## Elliptic curves in class 87120.ds

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
87120.ds1 87120ck2 $$[0, 0, 0, -257367, -50213306]$$ $$5702413264/5445$$ $$1800203031348480$$ $$[2]$$ $$491520$$ $$1.8488$$
87120.ds2 87120ck1 $$[0, 0, 0, -12342, -1159301]$$ $$-10061824/22275$$ $$-460279184151600$$ $$[2]$$ $$245760$$ $$1.5023$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 87120.ds have rank $$0$$.

## Complex multiplication

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

## Modular form 87120.2.a.ds

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.