# Properties

 Label 308550fs Number of curves 2 Conductor 308550 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("308550.fs1")

sage: E.isogeny_class()

## Elliptic curves in class 308550fs

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
308550.fs2 308550fs1 [1, 1, 1, -2662063, -737374219]  15482880 $$\Gamma_0(N)$$-optimal
308550.fs1 308550fs2 [1, 1, 1, -35574063, -81635070219]  30965760

## Rank

sage: E.rank()

The elliptic curves in class 308550fs have rank $$0$$.

## Modular form 308550.2.a.fs

sage: E.q_eigenform(10)

$$q + q^{2} - q^{3} + q^{4} - q^{6} - 2q^{7} + q^{8} + q^{9} - q^{12} - 4q^{13} - 2q^{14} + q^{16} + q^{17} + q^{18} + 6q^{19} + O(q^{20})$$

## 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. 