# Properties

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

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

sage: E.isogeny_class()

## Elliptic curves in class 235200.k

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
235200.k1 235200k2 $$[0, -1, 0, -27480833, 58676769537]$$ $$-7620530425/526848$$ $$-158676839301120000000000$$ $$[]$$ $$29859840$$ $$3.2027$$
235200.k2 235200k1 $$[0, -1, 0, 1919167, 82569537]$$ $$2595575/1512$$ $$-455386337280000000000$$ $$[]$$ $$9953280$$ $$2.6534$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## 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 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. 