# Properties

 Label 235200.p Number of curves $2$ Conductor $235200$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("235200.p1")

sage: E.isogeny_class()

## Elliptic curves in class 235200.p

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
235200.p1 235200p2 [0, -1, 0, -11252400833, -459422604230463] [] 174182400
235200.p2 235200p1 [0, -1, 0, -139200833, -627478070463] [] 58060800 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Modular form 235200.2.a.p

sage: E.q_eigenform(10)

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

## 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 LMFDB 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 LMFDB labels. 