# Properties

 Label 11200.be Number of curves $3$ Conductor $11200$ CM no Rank $1$ Graph

# Learn more

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

sage: E.isogeny_class()

## Elliptic curves in class 11200.be

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
11200.be1 11200cn3 $$[0, -1, 0, -13133, 610387]$$ $$-250523582464/13671875$$ $$-13671875000000$$ $$[]$$ $$20736$$ $$1.2788$$
11200.be2 11200cn1 $$[0, -1, 0, -133, -613]$$ $$-262144/35$$ $$-35000000$$ $$[]$$ $$2304$$ $$0.18014$$ $$\Gamma_0(N)$$-optimal
11200.be3 11200cn2 $$[0, -1, 0, 867, 1387]$$ $$71991296/42875$$ $$-42875000000$$ $$[]$$ $$6912$$ $$0.72945$$

## Rank

sage: E.rank()

The elliptic curves in class 11200.be have rank $$1$$.

## Complex multiplication

The elliptic curves in class 11200.be do not have complex multiplication.

## Modular form 11200.2.a.be

sage: E.q_eigenform(10)

$$q - q^{3} + q^{7} - 2q^{9} - 3q^{11} + 5q^{13} - 3q^{17} + 2q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.