# Properties

 Label 28322t Number of curves 4 Conductor 28322 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("28322.bb1")

sage: E.isogeny_class()

## Elliptic curves in class 28322t

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
28322.bb3 28322t1 [1, -1, 1, -264634, -51489175]  221184 $$\Gamma_0(N)$$-optimal
28322.bb2 28322t2 [1, -1, 1, -547854, 78338873] [2, 2] 442368
28322.bb4 28322t3 [1, -1, 1, 1859516, 579071833]  884736
28322.bb1 28322t4 [1, -1, 1, -7486744, 7883202345]  884736

## Rank

sage: E.rank()

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

## Modular form 28322.2.a.bb

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels. 