# Properties

 Label 9360.bn Number of curves $4$ Conductor $9360$ CM no Rank $0$ Graph

# Related objects

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

E.isogeny_class()

## Elliptic curves in class 9360.bn

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
9360.bn1 9360bs3 $$[0, 0, 0, -69627, -7070294]$$ $$12501706118329/2570490$$ $$7675442012160$$ $$[2]$$ $$24576$$ $$1.4695$$
9360.bn2 9360bs2 $$[0, 0, 0, -4827, -84854]$$ $$4165509529/1368900$$ $$4087513497600$$ $$[2, 2]$$ $$12288$$ $$1.1229$$
9360.bn3 9360bs1 $$[0, 0, 0, -1947, 32074]$$ $$273359449/9360$$ $$27948810240$$ $$[2]$$ $$6144$$ $$0.77634$$ $$\Gamma_0(N)$$-optimal
9360.bn4 9360bs4 $$[0, 0, 0, 13893, -582806]$$ $$99317171591/106616250$$ $$-318354416640000$$ $$[2]$$ $$24576$$ $$1.4695$$

## Rank

sage: E.rank()

The elliptic curves in class 9360.bn have rank $$0$$.

## Complex multiplication

The elliptic curves in class 9360.bn do not have complex multiplication.

## Modular form9360.2.a.bn

sage: E.q_eigenform(10)

$$q + q^{5} - q^{13} + 6 q^{17} + O(q^{20})$$

## 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.