# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("28322.q1")

sage: E.isogeny_class()

## Elliptic curves in class 28322.q

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
28322.q1 28322bb2 [1, 0, 0, -9912995, -11989610879]  3096576
28322.q2 28322bb1 [1, 0, 0, -849955, -35461119]  1548288 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Modular form 28322.2.a.q

sage: E.q_eigenform(10)

$$q + q^{2} - 2q^{3} + q^{4} - 4q^{5} - 2q^{6} + q^{8} + q^{9} - 4q^{10} + 6q^{11} - 2q^{12} + 2q^{13} + 8q^{15} + q^{16} + q^{18} + O(q^{20})$$

## 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. 