# Properties

 Label 33800u Number of curves 2 Conductor 33800 CM no Rank 2 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("33800.e1")

sage: E.isogeny_class()

## Elliptic curves in class 33800u

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
33800.e1 33800u1 [0, 1, 0, -85908, -9569312] [2] 129024 $$\Gamma_0(N)$$-optimal
33800.e2 33800u2 [0, 1, 0, -1408, -27483312] [2] 258048

## Rank

sage: E.rank()

The elliptic curves in class 33800u have rank $$2$$.

## Modular form 33800.2.a.e

sage: E.q_eigenform(10)

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

## 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 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.