# Properties

 Label 346560.ko Number of curves $2$ Conductor $346560$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("ko1")

sage: E.isogeny_class()

## Elliptic curves in class 346560.ko

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
346560.ko1 346560ko2 $$[0, 1, 0, -233345, -43463457]$$ $$781484460931/900$$ $$1618241126400$$ $$$$ $$1474560$$ $$1.6267$$
346560.ko2 346560ko1 $$[0, 1, 0, -14465, -694305]$$ $$-186169411/6480$$ $$-11651336110080$$ $$$$ $$737280$$ $$1.2801$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 346560.ko have rank $$1$$.

## Complex multiplication

The elliptic curves in class 346560.ko do not have complex multiplication.

## Modular form 346560.2.a.ko

sage: E.q_eigenform(10)

$$q + q^{3} + q^{5} + 2q^{7} + q^{9} + 2q^{13} + q^{15} - 6q^{17} + O(q^{20})$$ ## 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. 