# Properties

 Label 187200.lu Number of curves $2$ Conductor $187200$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("lu1")

sage: E.isogeny_class()

## Elliptic curves in class 187200.lu

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
187200.lu1 187200bp2 $$[0, 0, 0, -92460, -1841200]$$ $$3659383421/2056392$$ $$49122828877824000$$ $$$$ $$1179648$$ $$1.8929$$
187200.lu2 187200bp1 $$[0, 0, 0, 22740, -228400]$$ $$54439939/32448$$ $$-775113670656000$$ $$$$ $$589824$$ $$1.5463$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 187200.lu have rank $$0$$.

## Complex multiplication

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

## Modular form 187200.2.a.lu

sage: E.q_eigenform(10)

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