# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("259920.gb1")

sage: E.isogeny_class()

## Elliptic curves in class 259920.gb

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
259920.gb1 259920gb2 [0, 0, 0, -3712467, 2752865426]  3932160
259920.gb2 259920gb1 [0, 0, 0, -210387, 51360914]  1966080 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Modular form 259920.2.a.gb

sage: E.q_eigenform(10)

$$q + q^{5} + 2q^{7} - 2q^{13} + 2q^{17} + O(q^{20})$$

## 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. 