# Properties

 Label 229320.bm Number of curves $2$ Conductor $229320$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("bm1")

sage: E.isogeny_class()

## Elliptic curves in class 229320.bm

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
229320.bm1 229320bt2 $$[0, 0, 0, -10503003, -9590309498]$$ $$4253577358972/1142578125$$ $$34418802018510000000000$$ $$[2]$$ $$17203200$$ $$3.0326$$
229320.bm2 229320bt1 $$[0, 0, 0, -9700383, -11627519582]$$ $$13404187799728/1584375$$ $$11931851366416800000$$ $$[2]$$ $$8601600$$ $$2.6860$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 229320.bm have rank $$0$$.

## Complex multiplication

The elliptic curves in class 229320.bm do not have complex multiplication.

## Modular form 229320.2.a.bm

sage: E.q_eigenform(10)

$$q - q^{5} - q^{13} + 4 q^{17} + 6 q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.