# Properties

 Label 28322d Number of curves 2 Conductor 28322 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("28322.g1")

sage: E.isogeny_class()

## Elliptic curves in class 28322d

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
28322.g2 28322d1 [1, -1, 0, 25667, -796335]  110592 $$\Gamma_0(N)$$-optimal
28322.g1 28322d2 [1, -1, 0, -115943, -6658989]  221184

## Rank

sage: E.rank()

The elliptic curves in class 28322d have rank $$0$$.

## Modular form 28322.2.a.g

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels. 