# Properties

 Label 388080bm Number of curves 4 Conductor 388080 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("388080.bm1")

sage: E.isogeny_class()

## Elliptic curves in class 388080bm

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
388080.bm3 388080bm1 [0, 0, 0, -3535203, 2221492322]  14155776 $$\Gamma_0(N)$$-optimal
388080.bm2 388080bm2 [0, 0, 0, -14965923, -20070697822] [2, 2] 28311552
388080.bm4 388080bm3 [0, 0, 0, 19961277, -99823466302]  56623104
388080.bm1 388080bm4 [0, 0, 0, -232784643, -1367018098558]  56623104

## Rank

sage: E.rank()

The elliptic curves in class 388080bm have rank $$0$$.

## Modular form 388080.2.a.bm

sage: E.q_eigenform(10)

$$q - q^{5} - q^{11} - 2q^{13} + 2q^{17} + 4q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels. 