# Properties

 Label 259920gw Number of curves $2$ Conductor $259920$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("259920.gw1")

sage: E.isogeny_class()

## Elliptic curves in class 259920gw

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
259920.gw2 259920gw1 [0, 0, 0, -340347, -3872086]  5898240 $$\Gamma_0(N)$$-optimal
259920.gw1 259920gw2 [0, 0, 0, -3842427, -2891687254]  11796480

## Rank

sage: E.rank()

The elliptic curves in class 259920gw have rank $$0$$.

## Modular form 259920.2.a.gw

sage: E.q_eigenform(10)

$$q + q^{5} + 4q^{7} + 6q^{11} - 4q^{13} - 6q^{17} + O(q^{20})$$

## 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. 