# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("28322.y1")

sage: E.isogeny_class()

## Elliptic curves in class 28322.y

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
28322.y1 28322r1 [1, -1, 1, -37225, -2602071]  98304 $$\Gamma_0(N)$$-optimal
28322.y2 28322r2 [1, -1, 1, 29415, -10945399]  196608

## Rank

sage: E.rank()

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

## Modular form 28322.2.a.y

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 LMFDB 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 LMFDB labels. 