# Properties

 Label 228888u Number of curves 4 Conductor 228888 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("228888.bz1")

sage: E.isogeny_class()

## Elliptic curves in class 228888u

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
228888.bz3 228888u1 [0, 0, 0, -32079, 2132242] [2] 589824 $$\Gamma_0(N)$$-optimal
228888.bz2 228888u2 [0, 0, 0, -84099, -6534290] [2, 2] 1179648
228888.bz4 228888u3 [0, 0, 0, 228021, -43676570] [2] 2359296
228888.bz1 228888u4 [0, 0, 0, -1228539, -524050058] [2] 2359296

## Rank

sage: E.rank()

The elliptic curves in class 228888u have rank $$0$$.

## Modular form 228888.2.a.bz

sage: E.q_eigenform(10)

$$q + 2q^{5} + q^{11} + 2q^{13} + O(q^{20})$$

## 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.