# Properties

 Label 118580m Number of curves 4 Conductor 118580 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("118580.ba1")

sage: E.isogeny_class()

## Elliptic curves in class 118580m

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
118580.ba4 118580m1 [0, -1, 0, -268781, 52624706] [2] 1244160 $$\Gamma_0(N)$$-optimal
118580.ba3 118580m2 [0, -1, 0, -594876, -99596440] [2] 2488320
118580.ba2 118580m3 [0, -1, 0, -2640381, -1629669754] [2] 3732480
118580.ba1 118580m4 [0, -1, 0, -42097876, -105118787640] [2] 7464960

## Rank

sage: E.rank()

The elliptic curves in class 118580m have rank $$0$$.

## Modular form 118580.2.a.ba

sage: E.q_eigenform(10)

$$q + 2q^{3} - q^{5} + q^{9} - 4q^{13} - 2q^{15} - 4q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with Cremona labels.