# Properties

 Label 8820j Number of curves 4 Conductor 8820 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("8820.g1")

sage: E.isogeny_class()

## Elliptic curves in class 8820j

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
8820.g3 8820j1 [0, 0, 0, -588, 3773]  4320 $$\Gamma_0(N)$$-optimal
8820.g4 8820j2 [0, 0, 0, 1617, 25382]  8640
8820.g1 8820j3 [0, 0, 0, -18228, -947023]  12960
8820.g2 8820j4 [0, 0, 0, -16023, -1184722]  25920

## Rank

sage: E.rank()

The elliptic curves in class 8820j have rank $$0$$.

## Modular form8820.2.a.g

sage: E.q_eigenform(10)

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

## 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 Cremona 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 Cremona labels. 