# Properties

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

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("162450.cf1")

sage: E.isogeny_class()

## Elliptic curves in class 162450.cf

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
162450.cf1 162450eg2 [1, -1, 0, -6003792, 5649327616] [2] 11796480
162450.cf2 162450eg1 [1, -1, 0, -531792, 7695616] [2] 5898240 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Modular form 162450.2.a.cf

sage: E.q_eigenform(10)

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

## 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 LMFDB 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 LMFDB labels.