# Properties

 Label 180999d Number of curves $2$ Conductor $180999$ CM no Rank $2$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("d1")

sage: E.isogeny_class()

## Elliptic curves in class 180999d

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
180999.d1 180999d1 $$[1, -1, 1, -692087, -221319250]$$ $$10418796526321/6390657$$ $$22487084447440977$$ $$$$ $$3010560$$ $$2.0804$$ $$\Gamma_0(N)$$-optimal
180999.d2 180999d2 $$[1, -1, 1, -562802, -306647350]$$ $$-5602762882081/8312741073$$ $$-29250405787427195553$$ $$$$ $$6021120$$ $$2.4270$$

## Rank

sage: E.rank()

The elliptic curves in class 180999d have rank $$2$$.

## Complex multiplication

The elliptic curves in class 180999d do not have complex multiplication.

## Modular form 180999.2.a.d

sage: E.q_eigenform(10)

$$q - q^{2} - q^{4} - 4q^{5} - q^{7} + 3q^{8} + 4q^{10} - 4q^{11} + q^{14} - q^{16} - q^{17} + O(q^{20})$$ ## 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. 