# Properties

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

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("235200.i1")

sage: E.isogeny_class()

## Elliptic curves in class 235200i

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
235200.i2 235200i1 [0, -1, 0, 8167, -2543463] [2] 1382400 $$\Gamma_0(N)$$-optimal
235200.i1 235200i2 [0, -1, 0, -236833, -42478463] [2] 2764800

## Rank

sage: E.rank()

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

## Modular form 235200.2.a.i

sage: E.q_eigenform(10)

$$q - q^{3} + q^{9} - 6q^{11} - 2q^{13} + 6q^{17} - 4q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.