# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("259920.gy1")

sage: E.isogeny_class()

## Elliptic curves in class 259920.gy

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
259920.gy1 259920gy2 [0, 0, 0, -1387116147, 19834082875186]  224133120
259920.gy2 259920gy1 [0, 0, 0, -122865267, 26558637874]  112066560 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Modular form 259920.2.a.gy

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 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. 