# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("162450.ek1")

sage: E.isogeny_class()

## Elliptic curves in class 162450.ek

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
162450.ek1 162450bl2 [1, -1, 1, -5800730, -5375240103]  3932160
162450.ek2 162450bl1 [1, -1, 1, -328730, -100232103]  1966080 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Modular form 162450.2.a.ek

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 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. 