# Properties

 Label 259920.gc Number of curves $2$ Conductor $259920$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("259920.gc1")

sage: E.isogeny_class()

## Elliptic curves in class 259920.gc

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
259920.gc1 259920gc2 [0, 0, 0, -1340200587, -18881903956934] [2] 74711040
259920.gc2 259920gc1 [0, 0, 0, -75949707, -352284509126] [2] 37355520 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Modular form 259920.2.a.gc

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.