# Properties

 Label 235200k Number of curves 2 Conductor 235200 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("235200.k1")

sage: E.isogeny_class()

## Elliptic curves in class 235200k

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
235200.k2 235200k1 [0, -1, 0, 1919167, 82569537] [] 9953280 $$\Gamma_0(N)$$-optimal
235200.k1 235200k2 [0, -1, 0, -27480833, 58676769537] [] 29859840

## Rank

sage: E.rank()

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

## Modular form 235200.2.a.k

sage: E.q_eigenform(10)

$$q - q^{3} + q^{9} - 6q^{11} + q^{13} + 3q^{17} - 4q^{19} + O(q^{20})$$

## 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 Cremona numbering.

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels. 