# Properties

 Label 28224.bn Number of curves $4$ Conductor $28224$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
E = EllipticCurve("bn1")

E.isogeny_class()

## Elliptic curves in class 28224.bn

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
28224.bn1 28224fz4 $$[0, 0, 0, -198156, 31813936]$$ $$306182024/21609$$ $$60729593321521152$$ $$[2]$$ $$196608$$ $$1.9678$$
28224.bn2 28224fz2 $$[0, 0, 0, -39396, -2414720]$$ $$19248832/3969$$ $$1394301887483904$$ $$[2, 2]$$ $$98304$$ $$1.6212$$
28224.bn3 28224fz1 $$[0, 0, 0, -37191, -2760464]$$ $$1036433728/63$$ $$345808999872$$ $$[2]$$ $$49152$$ $$1.2746$$ $$\Gamma_0(N)$$-optimal
28224.bn4 28224fz3 $$[0, 0, 0, 84084, -14515760]$$ $$23393656/45927$$ $$-129072517584224256$$ $$[2]$$ $$196608$$ $$1.9678$$

## Rank

sage: E.rank()

The elliptic curves in class 28224.bn have rank $$0$$.

## Complex multiplication

The elliptic curves in class 28224.bn do not have complex multiplication.

## Modular form 28224.2.a.bn

sage: E.q_eigenform(10)

$$q - 2 q^{5} + 2 q^{13} + 2 q^{17} - 4 q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.