# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("28322.d1")

sage: E.isogeny_class()

## Elliptic curves in class 28322i

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
28322.d1 28322i1 [1, 0, 1, -1307, -20688] [] 34560 $$\Gamma_0(N)$$-optimal
28322.d2 28322i2 [1, 0, 1, 8808, 80462] [] 103680

## Rank

sage: E.rank()

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

## Modular form 28322.2.a.d

sage: E.q_eigenform(10)

$$q - q^{2} - 2q^{3} + q^{4} + 3q^{5} + 2q^{6} - q^{8} + q^{9} - 3q^{10} - 2q^{12} - 2q^{13} - 6q^{15} + q^{16} - q^{18} + 7q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels. 