# Properties

 Label 424830.gs Number of curves $2$ Conductor $424830$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("424830.gs1")

sage: E.isogeny_class()

## Elliptic curves in class 424830.gs

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
424830.gs1 424830gs1 [1, 0, 0, -4341, -42435] [2] 946176 $$\Gamma_0(N)$$-optimal
424830.gs2 424830gs2 [1, 0, 0, 15889, -321609] [2] 1892352

## Rank

sage: E.rank()

The elliptic curves in class 424830.gs have rank $$0$$.

## Modular form 424830.2.a.gs

sage: E.q_eigenform(10)

$$q + q^{2} + q^{3} + q^{4} - q^{5} + q^{6} + q^{8} + q^{9} - q^{10} - 2q^{11} + q^{12} + 2q^{13} - q^{15} + q^{16} + q^{18} + O(q^{20})$$

## 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.