# Properties

 Label 388080.oq Number of curves $2$ Conductor $388080$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("oq1")

sage: E.isogeny_class()

## Elliptic curves in class 388080.oq

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
388080.oq1 388080oq2 $$[0, 0, 0, -189032592, 18912291835696]$$ $$-2126464142970105856/438611057788643355$$ $$-154083201246162036370538311680$$ $$[]$$ $$460800000$$ $$4.2799$$
388080.oq2 388080oq1 $$[0, 0, 0, -63082992, -225841753424]$$ $$-79028701534867456/16987307596875$$ $$-5967607721237710732800000$$ $$[]$$ $$92160000$$ $$3.4752$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 388080.oq have rank $$0$$.

## Complex multiplication

The elliptic curves in class 388080.oq do not have complex multiplication.

## Modular form 388080.2.a.oq

sage: E.q_eigenform(10)

$$q + q^{5} + q^{11} + 6q^{13} - 7q^{17} - 5q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.