# Properties

 Label 2366j Number of curves 6 Conductor 2366 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("2366.j1")

sage: E.isogeny_class()

## Elliptic curves in class 2366j

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
2366.j5 2366j1 [1, 0, 0, -88, 636]  720 $$\Gamma_0(N)$$-optimal
2366.j4 2366j2 [1, 0, 0, -1778, 28690]  1440
2366.j6 2366j3 [1, 0, 0, 757, -13391]  2160
2366.j3 2366j4 [1, 0, 0, -6003, -147239]  4320
2366.j2 2366j5 [1, 0, 0, -28818, -1890812]  6480
2366.j1 2366j6 [1, 0, 0, -461458, -120693756]  12960

## Rank

sage: E.rank()

The elliptic curves in class 2366j have rank $$0$$.

## Modular form2366.2.a.j

sage: E.q_eigenform(10)

$$q + q^{2} - 2q^{3} + q^{4} - 2q^{6} - q^{7} + q^{8} + q^{9} - 2q^{12} - q^{14} + q^{16} + 6q^{17} + q^{18} - 2q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrrrr} 1 & 2 & 3 & 6 & 9 & 18 \\ 2 & 1 & 6 & 3 & 18 & 9 \\ 3 & 6 & 1 & 2 & 3 & 6 \\ 6 & 3 & 2 & 1 & 6 & 3 \\ 9 & 18 & 3 & 6 & 1 & 2 \\ 18 & 9 & 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels. 