# Properties

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

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("ox1")

sage: E.isogeny_class()

## Elliptic curves in class 235200.ox

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
235200.ox1 235200ox2 $$[0, 1, 0, -1099233, 468974463]$$ $$-7620530425/526848$$ $$-10155317715271680000$$ $$[]$$ $$5971968$$ $$2.3980$$
235200.ox2 235200ox1 $$[0, 1, 0, 76767, 691263]$$ $$2595575/1512$$ $$-29144725585920000$$ $$[]$$ $$1990656$$ $$1.8487$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 235200.ox have rank $$2$$.

## Complex multiplication

The elliptic curves in class 235200.ox do not have complex multiplication.

## Modular form 235200.2.a.ox

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 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.