# Properties

 Label 162288fh Number of curves $2$ Conductor $162288$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("fh1")

sage: E.isogeny_class()

## Elliptic curves in class 162288fh

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
162288.dp2 162288fh1 $$[0, 0, 0, -12495, -690802]$$ $$-9826000/3703$$ $$-81303538192128$$ $$$$ $$368640$$ $$1.3789$$ $$\Gamma_0(N)$$-optimal
162288.dp1 162288fh2 $$[0, 0, 0, -215355, -38463334]$$ $$12576878500/1127$$ $$98978220407808$$ $$$$ $$737280$$ $$1.7255$$

## Rank

sage: E.rank()

The elliptic curves in class 162288fh have rank $$0$$.

## Complex multiplication

The elliptic curves in class 162288fh do not have complex multiplication.

## Modular form 162288.2.a.fh

sage: E.q_eigenform(10)

$$q + 4q^{11} - 6q^{13} + O(q^{20})$$ ## 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 Cremona 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 Cremona labels. 