# Properties

 Label 235200.zm Number of curves $2$ Conductor $235200$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("235200.zm1")

sage: E.isogeny_class()

## Elliptic curves in class 235200.zm

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
235200.zm1 235200zm1 [0, 1, 0, -24033, 540063] [2] 884736 $$\Gamma_0(N)$$-optimal
235200.zm2 235200zm2 [0, 1, 0, 87967, 4236063] [2] 1769472

## Rank

sage: E.rank()

The elliptic curves in class 235200.zm have rank $$0$$.

## Modular form 235200.2.a.zm

sage: E.q_eigenform(10)

$$q + q^{3} + q^{9} + 2q^{11} + 2q^{13} + 4q^{17} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.