# Properties

 Label 235200.sd Number of curves $2$ Conductor $235200$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("235200.sd1")

sage: E.isogeny_class()

## Elliptic curves in class 235200.sd

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
235200.sd1 235200sd1 [0, 1, 0, -1177633, 187596863] [2] 6193152 $$\Gamma_0(N)$$-optimal
235200.sd2 235200sd2 [0, 1, 0, 4310367, 1444348863] [2] 12386304

## Rank

sage: E.rank()

The elliptic curves in class 235200.sd have rank $$1$$.

## Modular form 235200.2.a.sd

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.