# Properties

 Label 71630x Number of curves 2 Conductor 71630 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("71630.v1")

sage: E.isogeny_class()

## Elliptic curves in class 71630x

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
71630.v2 71630x1 [1, -1, 1, -265716552, 1667217712779]  26254592 $$\Gamma_0(N)$$-optimal
71630.v1 71630x2 [1, -1, 1, -6564370452, -204561760368501] [] 183782144

## Rank

sage: E.rank()

The elliptic curves in class 71630x have rank $$1$$.

## Modular form 71630.2.a.v

sage: E.q_eigenform(10)

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

## 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 Cremona 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 Cremona labels. 