# Properties

 Label 187200.pe Number of curves $2$ Conductor $187200$ CM no Rank $1$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("pe1")

sage: E.isogeny_class()

## Elliptic curves in class 187200.pe

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
187200.pe1 187200bw2 $$[0, 0, 0, -8940, 106000]$$ $$26463592/13689$$ $$40875134976000$$ $$$$ $$458752$$ $$1.3038$$
187200.pe2 187200bw1 $$[0, 0, 0, -7140, 232000]$$ $$107850176/117$$ $$43670016000$$ $$$$ $$229376$$ $$0.95725$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 187200.2.a.pe

sage: E.q_eigenform(10)

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