# Properties

 Label 33800m Number of curves 2 Conductor 33800 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("33800.n1")

sage: E.isogeny_class()

## Elliptic curves in class 33800m

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
33800.n2 33800m1 [0, 0, 0, -5915, -109850]  53760 $$\Gamma_0(N)$$-optimal
33800.n1 33800m2 [0, 0, 0, -39715, 2965950]  107520

## Rank

sage: E.rank()

The elliptic curves in class 33800m have rank $$0$$.

## Modular form 33800.2.a.n

sage: E.q_eigenform(10)

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

## 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. 