# Properties

 Label 71058.j Number of curves 2 Conductor 71058 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("71058.j1")

sage: E.isogeny_class()

## Elliptic curves in class 71058.j

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
71058.j1 71058k2 [1, 0, 0, -7072, 78524] [] 256896
71058.j2 71058k1 [1, 0, 0, -5692, 164816]  85632 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 71058.j have rank $$0$$.

## Modular form 71058.2.a.j

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 