# Properties

 Label 333270dh Number of curves $2$ Conductor $333270$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("dh1")

sage: E.isogeny_class()

## Elliptic curves in class 333270dh

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
333270.dh1 333270dh1 $$[1, -1, 1, -6071168, -5646794093]$$ $$8493409990827/185150000$$ $$539488293150073050000$$ $$[2]$$ $$16220160$$ $$2.7664$$ $$\Gamma_0(N)$$-optimal
333270.dh2 333270dh2 $$[1, -1, 1, 499012, -17231335469]$$ $$4716275733/44023437500$$ $$-128275069702802695312500$$ $$[2]$$ $$32440320$$ $$3.1129$$

## Rank

sage: E.rank()

The elliptic curves in class 333270dh have rank $$1$$.

## Complex multiplication

The elliptic curves in class 333270dh do not have complex multiplication.

## Modular form 333270.2.a.dh

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} - q^{5} - q^{7} + q^{8} - q^{10} + 2q^{11} + 2q^{13} - q^{14} + q^{16} + 2q^{17} + 4q^{19} + O(q^{20})$$

## 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 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.