# Properties

 Label 71058.n Number of curves 2 Conductor 71058 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("71058.n1")

sage: E.isogeny_class()

## Elliptic curves in class 71058.n

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
71058.n1 71058j2 [1, 0, 0, -10797, 430917]  86016
71058.n2 71058j1 [1, 0, 0, -657, 7065]  43008 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 71058.n have rank $$1$$.

## Modular form 71058.2.a.n

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 