# Properties

 Label 333270da Number of curves $2$ Conductor $333270$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("da1")

sage: E.isogeny_class()

## Elliptic curves in class 333270da

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
333270.da1 333270da1 $$[1, -1, 1, -111983, 7981031]$$ $$1439069689/579600$$ $$62549367321747600$$ $$$$ $$3244032$$ $$1.9209$$ $$\Gamma_0(N)$$-optimal
333270.da2 333270da2 $$[1, -1, 1, 364117, 57685871]$$ $$49471280711/41992020$$ $$-4531701662460613620$$ $$$$ $$6488064$$ $$2.2674$$

## Rank

sage: E.rank()

The elliptic curves in class 333270da have rank $$0$$.

## Complex multiplication

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

## Modular form 333270.2.a.da

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} - q^{5} - q^{7} + q^{8} - q^{10} - 2q^{11} + 4q^{13} - q^{14} + q^{16} - 6q^{17} + 4q^{19} + O(q^{20})$$ ## 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. 