# Properties

 Label 32487l Number of curves $6$ Conductor $32487$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("32487.f1")

sage: E.isogeny_class()

## Elliptic curves in class 32487l

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
32487.f4 32487l1 [1, 0, 0, -26412, -1654353] [2] 49152 $$\Gamma_0(N)$$-optimal
32487.f3 32487l2 [1, 0, 0, -26657, -1622160] [2, 2] 98304
32487.f5 32487l3 [1, 0, 0, 10828, -5812983] [2] 196608
32487.f2 32487l4 [1, 0, 0, -68062, 4629995] [2, 2] 196608
32487.f6 32487l5 [1, 0, 0, 189923, 31408838] [2] 393216
32487.f1 32487l6 [1, 0, 0, -988527, 378154692] [2] 393216

## Rank

sage: E.rank()

The elliptic curves in class 32487l have rank $$1$$.

## Modular form 32487.2.a.f

sage: E.q_eigenform(10)

$$q - q^{2} + q^{3} - q^{4} + 2q^{5} - q^{6} + 3q^{8} + q^{9} - 2q^{10} + 4q^{11} - q^{12} - q^{13} + 2q^{15} - q^{16} - q^{17} - q^{18} + 4q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.