# Properties

 Label 16245.k Number of curves $2$ Conductor $16245$ CM no Rank $0$ Graph

# Related objects

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

E.isogeny_class()

## Elliptic curves in class 16245.k

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
16245.k1 16245k2 $$[1, -1, 0, -303849, -62723970]$$ $$90458382169/2671875$$ $$91635819993421875$$ $$[2]$$ $$138240$$ $$2.0319$$
16245.k2 16245k1 $$[1, -1, 0, 4806, -3277017]$$ $$357911/135375$$ $$-4642881546333375$$ $$[2]$$ $$69120$$ $$1.6853$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 16245.k have rank $$0$$.

## Complex multiplication

The elliptic curves in class 16245.k do not have complex multiplication.

## Modular form16245.2.a.k

sage: E.q_eigenform(10)

$$q + q^{2} - q^{4} + q^{5} - 2 q^{7} - 3 q^{8} + q^{10} + 2 q^{11} + 4 q^{13} - 2 q^{14} - q^{16} - 2 q^{17} + O(q^{20})$$

## 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.