# Properties

 Label 99450cw Number of curves 2 Conductor 99450 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("99450.de1")

sage: E.isogeny_class()

## Elliptic curves in class 99450cw

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
99450.de1 99450cw1 [1, -1, 1, -3064505, -2040542503]  2949120 $$\Gamma_0(N)$$-optimal
99450.de2 99450cw2 [1, -1, 1, -472505, -5384222503]  5898240

## Rank

sage: E.rank()

The elliptic curves in class 99450cw have rank $$0$$.

## Modular form 99450.2.a.de

sage: E.q_eigenform(10)

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

## 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. 