# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("28322.j1")

sage: E.isogeny_class()

## Elliptic curves in class 28322.j

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
28322.j1 28322b1 [1, 1, 0, -64019, 7031879] [] 241920 $$\Gamma_0(N)$$-optimal
28322.j2 28322b2 [1, 1, 0, 431616, -27166936] [] 725760

## Rank

sage: E.rank()

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

## Modular form 28322.2.a.j

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 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. 