# Properties

 Label 28322q Number of curves 2 Conductor 28322 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("28322.z1")

sage: E.isogeny_class()

## Elliptic curves in class 28322q

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
28322.z1 28322q1 [1, -1, 1, -10757935, -12827005257]  1671168 $$\Gamma_0(N)$$-optimal
28322.z2 28322q2 [1, -1, 1, 8501025, -53740739881]  3342336

## Rank

sage: E.rank()

The elliptic curves in class 28322q have rank $$1$$.

## Modular form 28322.2.a.z

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} + q^{8} - 3q^{9} - 2q^{13} + q^{16} - 3q^{18} + 4q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels. 