# Properties

 Label 5610.bl Number of curves 2 Conductor 5610 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("5610.bl1")

sage: E.isogeny_class()

## Elliptic curves in class 5610.bl

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
5610.bl1 5610bk2 [1, 0, 0, -11760, 489600]  10752
5610.bl2 5610bk1 [1, 0, 0, -880, 4352]  5376 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 5610.bl have rank $$1$$.

## Modular form5610.2.a.bl

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 