# Properties

 Label 33600ce Number of curves 4 Conductor 33600 CM no Rank 0 Graph

# Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("33600.ej1")

sage: E.isogeny_class()

## Elliptic curves in class 33600ce

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
33600.ej3 33600ce1 [0, 1, 0, -4033, 92063] [2] 49152 $$\Gamma_0(N)$$-optimal
33600.ej2 33600ce2 [0, 1, 0, -12033, -395937] [2, 2] 98304
33600.ej4 33600ce3 [0, 1, 0, 27967, -2435937] [2] 196608
33600.ej1 33600ce4 [0, 1, 0, -180033, -29459937] [2] 196608

## Rank

sage: E.rank()

The elliptic curves in class 33600ce have rank $$0$$.

## Modular form 33600.2.a.ej

sage: E.q_eigenform(10)

$$q + q^{3} - q^{7} + q^{9} - 6q^{13} - 2q^{17} + 8q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.