# Properties

 Label 405600.k Number of curves $2$ Conductor $405600$ CM no Rank $0$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 405600.k

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
405600.k1 405600k1 $$[0, -1, 0, -2274458, 1320992412]$$ $$2156689088/81$$ $$48871441125000000$$ $$$$ $$8294400$$ $$2.2887$$ $$\Gamma_0(N)$$-optimal
405600.k2 405600k2 $$[0, -1, 0, -2168833, 1449115537]$$ $$-29218112/6561$$ $$-253349550792000000000$$ $$$$ $$16588800$$ $$2.6353$$

## Rank

sage: E.rank()

The elliptic curves in class 405600.k have rank $$0$$.

## Complex multiplication

The elliptic curves in class 405600.k do not have complex multiplication.

## Modular form 405600.2.a.k

sage: E.q_eigenform(10)

$$q - q^{3} - 4q^{7} + q^{9} + 8q^{19} + O(q^{20})$$ ## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 