# Properties

 Label 858.k Number of curves 2 Conductor 858 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("858.k1")

sage: E.isogeny_class()

## Elliptic curves in class 858.k

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
858.k1 858k1 [1, 0, 0, -5774401, 5346023177]  35280 $$\Gamma_0(N)$$-optimal
858.k2 858k2 [1, 0, 0, 16353089, -335543012233] [] 246960

## Rank

sage: E.rank()

The elliptic curves in class 858.k have rank $$0$$.

## Modular form858.2.a.k

sage: E.q_eigenform(10)

$$q + q^{2} + q^{3} + q^{4} - q^{5} + q^{6} + q^{7} + q^{8} + q^{9} - q^{10} + q^{11} + q^{12} - q^{13} + q^{14} - q^{15} + q^{16} + 4q^{17} + q^{18} + 6q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 