# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("28322.s1")

sage: E.isogeny_class()

## Elliptic curves in class 28322.s

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
28322.s1 28322bi1 [1, 1, 1, -99422, -12110253] [] 145152 $$\Gamma_0(N)$$-optimal
28322.s2 28322bi2 [1, 1, 1, 42188, -42698013] [] 435456

## Rank

sage: E.rank()

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

## Modular form 28322.2.a.s

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 