# Properties

 Label 187200.lj Number of curves $2$ Conductor $187200$ CM no Rank $1$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("lj1")

sage: E.isogeny_class()

## Elliptic curves in class 187200.lj

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
187200.lj1 187200fh2 $$[0, 0, 0, -662700, -186014000]$$ $$10779215329/1232010$$ $$3678762147840000000$$ $$[2]$$ $$3538944$$ $$2.2947$$
187200.lj2 187200fh1 $$[0, 0, 0, 57300, -14654000]$$ $$6967871/35100$$ $$-104808038400000000$$ $$[2]$$ $$1769472$$ $$1.9481$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 187200.lj have rank $$1$$.

## Complex multiplication

The elliptic curves in class 187200.lj do not have complex multiplication.

## Modular form 187200.2.a.lj

sage: E.q_eigenform(10)

$$q + 2q^{7} - 4q^{11} - q^{13} + 8q^{17} - 6q^{19} + O(q^{20})$$

## 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.