# Properties

 Label 33800.o Number of curves 4 Conductor 33800 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("33800.o1")

sage: E.isogeny_class()

## Elliptic curves in class 33800.o

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
33800.o1 33800a4 [0, 0, 0, -2378675, -1411023250]  516096
33800.o2 33800a2 [0, 0, 0, -181675, -11534250] [2, 2] 258048
33800.o3 33800a1 [0, 0, 0, -97175, 11534250]  129024 $$\Gamma_0(N)$$-optimal
33800.o4 33800a3 [0, 0, 0, 663325, -88429250]  516096

## Rank

sage: E.rank()

The elliptic curves in class 33800.o have rank $$1$$.

## Modular form 33800.2.a.o

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 