# Properties

 Label 1850.k Number of curves $4$ Conductor $1850$ CM no Rank $1$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 1850.k

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1850.k1 1850j3 $$[1, -1, 1, -9880, -375503]$$ $$6825481747209/46250$$ $$722656250$$ $$$$ $$1536$$ $$0.88123$$
1850.k2 1850j2 $$[1, -1, 1, -630, -5503]$$ $$1767172329/136900$$ $$2139062500$$ $$[2, 2]$$ $$768$$ $$0.53466$$
1850.k3 1850j1 $$[1, -1, 1, -130, 497]$$ $$15438249/2960$$ $$46250000$$ $$$$ $$384$$ $$0.18808$$ $$\Gamma_0(N)$$-optimal
1850.k4 1850j4 $$[1, -1, 1, 620, -25503]$$ $$1689410871/18741610$$ $$-292837656250$$ $$$$ $$1536$$ $$0.88123$$

## Rank

sage: E.rank()

The elliptic curves in class 1850.k have rank $$1$$.

## Complex multiplication

The elliptic curves in class 1850.k do not have complex multiplication.

## Modular form1850.2.a.k

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} + q^{8} - 3q^{9} - 4q^{11} - 2q^{13} + q^{16} + 2q^{17} - 3q^{18} - 4q^{19} + O(q^{20})$$ ## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 