# Properties

 Label 111090.be Number of curves $2$ Conductor $111090$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("be1")

sage: E.isogeny_class()

## Elliptic curves in class 111090.be

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
111090.be1 111090be1 $$[1, 0, 1, -12443, -295594]$$ $$1439069689/579600$$ $$85801601264400$$ $$[2]$$ $$405504$$ $$1.3715$$ $$\Gamma_0(N)$$-optimal
111090.be2 111090be2 $$[1, 0, 1, 40457, -2136514]$$ $$49471280711/41992020$$ $$-6216326011605780$$ $$[2]$$ $$811008$$ $$1.7181$$

## Rank

sage: E.rank()

The elliptic curves in class 111090.be have rank $$0$$.

## Complex multiplication

The elliptic curves in class 111090.be do not have complex multiplication.

## Modular form 111090.2.a.be

sage: E.q_eigenform(10)

$$q - q^{2} + q^{3} + q^{4} + q^{5} - q^{6} - q^{7} - q^{8} + q^{9} - q^{10} + 2q^{11} + q^{12} + 4q^{13} + q^{14} + q^{15} + q^{16} + 6q^{17} - q^{18} + 4q^{19} + O(q^{20})$$

## 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.