# Properties

 Label 87120.du Number of curves $2$ Conductor $87120$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("du1")

sage: E.isogeny_class()

## Elliptic curves in class 87120.du

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
87120.du1 87120gb2 $$[0, 0, 0, -431607, 109107394]$$ $$26894628304/9075$$ $$3000338385580800$$ $$$$ $$737280$$ $$1.9419$$
87120.du2 87120gb1 $$[0, 0, 0, -23232, 2194819]$$ $$-67108864/61875$$ $$-1278553289310000$$ $$$$ $$368640$$ $$1.5953$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 87120.du have rank $$1$$.

## Complex multiplication

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

## Modular form 87120.2.a.du

sage: E.q_eigenform(10)

$$q + q^{5} - 2q^{7} - 2q^{13} + 8q^{17} - 2q^{19} + O(q^{20})$$ ## 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. 