# Properties

 Label 202800fe Number of curves $2$ Conductor $202800$ CM no Rank $2$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("fe1")

sage: E.isogeny_class()

## Elliptic curves in class 202800fe

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
202800.bs2 202800fe1 $$[0, -1, 0, 268992, 148960512]$$ $$6967871/35100$$ $$-10842943737600000000$$ $$[2]$$ $$4644864$$ $$2.3347$$ $$\Gamma_0(N)$$-optimal
202800.bs1 202800fe2 $$[0, -1, 0, -3111008, 1893040512]$$ $$10779215329/1232010$$ $$380587325189760000000$$ $$[2]$$ $$9289728$$ $$2.6813$$

## Rank

sage: E.rank()

The elliptic curves in class 202800fe have rank $$2$$.

## Complex multiplication

The elliptic curves in class 202800fe do not have complex multiplication.

## Modular form 202800.2.a.fe

sage: E.q_eigenform(10)

$$q - q^{3} - 2q^{7} + q^{9} + 4q^{11} - 8q^{17} - 6q^{19} + O(q^{20})$$

## 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 Cremona 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 Cremona labels.