# Properties

 Label 162450dz Number of curves $2$ Conductor $162450$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("162450.bu1")

sage: E.isogeny_class()

## Elliptic curves in class 162450dz

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
162450.bu2 162450dz1 [1, -1, 0, -118671417, 688085349741] [2] 37355520 $$\Gamma_0(N)$$-optimal
162450.bu1 162450dz2 [1, -1, 0, -2094063417, 36879242181741] [2] 74711040

## Rank

sage: E.rank()

The elliptic curves in class 162450dz have rank $$0$$.

## Modular form 162450.2.a.bu

sage: E.q_eigenform(10)

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

## 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.