# Properties

 Label 1287.e Number of curves $6$ Conductor $1287$ CM no Rank $0$ Graph

# Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("1287.e1")

sage: E.isogeny_class()

## Elliptic curves in class 1287.e

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1287.e1 1287e3 [1, -1, 0, -61776, -5894451] [2] 2048
1287.e2 1287e5 [1, -1, 0, -27081, 1667790] [4] 4096
1287.e3 1287e4 [1, -1, 0, -4266, -70713] [2, 2] 2048
1287.e4 1287e2 [1, -1, 0, -3861, -91368] [2, 2] 1024
1287.e5 1287e1 [1, -1, 0, -216, -1701] [2] 512 $$\Gamma_0(N)$$-optimal
1287.e6 1287e6 [1, -1, 0, 12069, -492156] [2] 4096

## Rank

sage: E.rank()

The elliptic curves in class 1287.e have rank $$0$$.

## Modular form1287.2.a.e

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.