# Properties

 Label 9360o Number of curves $4$ Conductor $9360$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("o1")

sage: E.isogeny_class()

## Elliptic curves in class 9360o

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
9360.b4 9360o1 $$[0, 0, 0, -183, 3382]$$ $$-3631696/24375$$ $$-4548960000$$ $$[2]$$ $$6144$$ $$0.53654$$ $$\Gamma_0(N)$$-optimal
9360.b3 9360o2 $$[0, 0, 0, -4683, 123082]$$ $$15214885924/38025$$ $$28385510400$$ $$[2, 2]$$ $$12288$$ $$0.88311$$
9360.b2 9360o3 $$[0, 0, 0, -6483, 19762]$$ $$20183398562/11567205$$ $$17269744527360$$ $$[2]$$ $$24576$$ $$1.2297$$
9360.b1 9360o4 $$[0, 0, 0, -74883, 7887202]$$ $$31103978031362/195$$ $$291133440$$ $$[2]$$ $$24576$$ $$1.2297$$

## Rank

sage: E.rank()

The elliptic curves in class 9360o have rank $$1$$.

## Complex multiplication

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

## Modular form9360.2.a.o

sage: E.q_eigenform(10)

$$q - q^{5} - 4q^{7} + 4q^{11} + q^{13} - 6q^{17} + O(q^{20})$$

## 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 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.