# Properties

 Label 193200bm Number of curves $2$ Conductor $193200$ CM no Rank $0$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 193200bm

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
193200.gz1 193200bm1 $$[0, 1, 0, -9408, -196812]$$ $$1439069689/579600$$ $$37094400000000$$ $$$$ $$442368$$ $$1.3017$$ $$\Gamma_0(N)$$-optimal
193200.gz2 193200bm2 $$[0, 1, 0, 30592, -1396812]$$ $$49471280711/41992020$$ $$-2687489280000000$$ $$$$ $$884736$$ $$1.6482$$

## Rank

sage: E.rank()

The elliptic curves in class 193200bm have rank $$0$$.

## Complex multiplication

The elliptic curves in class 193200bm do not have complex multiplication.

## Modular form 193200.2.a.bm

sage: E.q_eigenform(10)

$$q + q^{3} + q^{7} + q^{9} + 2q^{11} - 4q^{13} + 6q^{17} + 4q^{19} + O(q^{20})$$ ## 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 Cremona 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 Cremona labels. 