# Properties

 Label 25872.bf Number of curves 6 Conductor 25872 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("25872.bf1")

sage: E.isogeny_class()

## Elliptic curves in class 25872.bf

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
25872.bf1 25872bx6 [0, -1, 0, -3542912, -2565598272] [2] 491520
25872.bf2 25872bx4 [0, -1, 0, -222672, -39559680] [2, 2] 245760
25872.bf3 25872bx2 [0, -1, 0, -30592, 1161280] [2, 2] 122880
25872.bf4 25872bx1 [0, -1, 0, -26672, 1684992] [2] 61440 $$\Gamma_0(N)$$-optimal
25872.bf5 25872bx5 [0, -1, 0, 24288, -122735808] [4] 491520
25872.bf6 25872bx3 [0, -1, 0, 98768, 8301952] [2] 245760

## Rank

sage: E.rank()

The elliptic curves in class 25872.bf have rank $$0$$.

## Modular form 25872.2.a.bf

sage: E.q_eigenform(10)

$$q - q^{3} + 2q^{5} + q^{9} + q^{11} - 6q^{13} - 2q^{15} - 2q^{17} + 4q^{19} + O(q^{20})$$

## 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 LMFDB numbering.

$$\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 4 & 8 \\ 2 & 1 & 2 & 4 & 2 & 4 \\ 4 & 2 & 1 & 2 & 4 & 2 \\ 8 & 4 & 2 & 1 & 8 & 4 \\ 4 & 2 & 4 & 8 & 1 & 8 \\ 8 & 4 & 2 & 4 & 8 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.