# Properties

 Label 162450v Number of curves $2$ Conductor $162450$ CM no Rank $1$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("162450.dd1")

sage: E.isogeny_class()

## Elliptic curves in class 162450v

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
162450.dd2 162450v1 [1, -1, 1, -50855, 4557647]  737280 $$\Gamma_0(N)$$-optimal
162450.dd1 162450v2 [1, -1, 1, -820355, 286194647]  1474560

## Rank

sage: E.rank()

The elliptic curves in class 162450v have rank $$1$$.

## Modular form 162450.2.a.dd

sage: E.q_eigenform(10)

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

## 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 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. 