# Properties

 Label 46800.fm Number of curves $4$ Conductor $46800$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("fm1")

sage: E.isogeny_class()

## Elliptic curves in class 46800.fm

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
46800.fm1 46800x4 $$[0, 0, 0, -1872075, 985900250]$$ $$31103978031362/195$$ $$4548960000000$$ $$[2]$$ $$589824$$ $$2.0344$$
46800.fm2 46800x3 $$[0, 0, 0, -162075, 2470250]$$ $$20183398562/11567205$$ $$269839758240000000$$ $$[2]$$ $$589824$$ $$2.0344$$
46800.fm3 46800x2 $$[0, 0, 0, -117075, 15385250]$$ $$15214885924/38025$$ $$443523600000000$$ $$[2, 2]$$ $$294912$$ $$1.6878$$
46800.fm4 46800x1 $$[0, 0, 0, -4575, 422750]$$ $$-3631696/24375$$ $$-71077500000000$$ $$[2]$$ $$147456$$ $$1.3413$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 46800.fm have rank $$0$$.

## Complex multiplication

The elliptic curves in class 46800.fm do not have complex multiplication.

## Modular form 46800.2.a.fm

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 LMFDB numbering.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.