# Properties

 Label 187200fz Number of curves $4$ Conductor $187200$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("fz1")

sage: E.isogeny_class()

## Elliptic curves in class 187200fz

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
187200.oz4 187200fz1 $$[0, 0, 0, -18300, 3382000]$$ $$-3631696/24375$$ $$-4548960000000000$$ $$$$ $$1179648$$ $$1.6878$$ $$\Gamma_0(N)$$-optimal
187200.oz3 187200fz2 $$[0, 0, 0, -468300, 123082000]$$ $$15214885924/38025$$ $$28385510400000000$$ $$[2, 2]$$ $$2359296$$ $$2.0344$$
187200.oz1 187200fz3 $$[0, 0, 0, -7488300, 7887202000]$$ $$31103978031362/195$$ $$291133440000000$$ $$$$ $$4718592$$ $$2.3810$$
187200.oz2 187200fz4 $$[0, 0, 0, -648300, 19762000]$$ $$20183398562/11567205$$ $$17269744527360000000$$ $$$$ $$4718592$$ $$2.3810$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 187200.2.a.fz

sage: E.q_eigenform(10)

$$q + 4q^{7} - 4q^{11} + q^{13} + 6q^{17} + O(q^{20})$$ ## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels. 