# Properties

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

Show commands: SageMath
E = EllipticCurve("bb1")

E.isogeny_class()

## Elliptic curves in class 5610.bb

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5610.bb1 5610bd2 $$[1, 1, 1, -880, 8777]$$ $$75370704203521/7497765000$$ $$7497765000$$ $$$$ $$4608$$ $$0.63133$$
5610.bb2 5610bd1 $$[1, 1, 1, -200, -1015]$$ $$885012508801/137332800$$ $$137332800$$ $$$$ $$2304$$ $$0.28476$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

The elliptic curves in class 5610.bb do not have complex multiplication.

## Modular form5610.2.a.bb

sage: E.q_eigenform(10)

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

## 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 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. 