# Properties

 Label 9360.b Number of curves $4$ Conductor $9360$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("b1")

sage: E.isogeny_class()

## Elliptic curves in class 9360.b

sage: E.isogeny_class().curves

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

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form9360.2.a.b

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 LMFDB numbering.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 