# Properties

 Label 104742.bv Number of curves 4 Conductor 104742 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("104742.bv1")

sage: E.isogeny_class()

## Elliptic curves in class 104742.bv

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
104742.bv1 104742bl3 [1, -1, 1, -383360, -90914461]  1140480
104742.bv2 104742bl4 [1, -1, 1, -192920, -181411549]  2280960
104742.bv3 104742bl1 [1, -1, 1, -26285, 1553681]  380160 $$\Gamma_0(N)$$-optimal
104742.bv4 104742bl2 [1, -1, 1, 21325, 6524165]  760320

## Rank

sage: E.rank()

The elliptic curves in class 104742.bv have rank $$0$$.

## Modular form 104742.2.a.bv

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} - 2q^{7} + q^{8} - q^{11} - 4q^{13} - 2q^{14} + q^{16} - 6q^{17} + 4q^{19} + O(q^{20})$$

## 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 LMFDB 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 LMFDB labels. 