# Properties

 Label 5610.bi Number of curves $4$ Conductor $5610$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
E = EllipticCurve("bi1")

E.isogeny_class()

## Elliptic curves in class 5610.bi

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5610.bi1 5610bg3 $$[1, 0, 0, -107371, 4812815]$$ $$136894171818794254129/69177425857031250$$ $$69177425857031250$$ $$[2]$$ $$81920$$ $$1.9239$$
5610.bi2 5610bg2 $$[1, 0, 0, -86801, 9827781]$$ $$72326626749631816849/69403061722500$$ $$69403061722500$$ $$[2, 2]$$ $$40960$$ $$1.5773$$
5610.bi3 5610bg1 $$[1, 0, 0, -86781, 9832545]$$ $$72276643492008825169/66646800$$ $$66646800$$ $$[4]$$ $$20480$$ $$1.2307$$ $$\Gamma_0(N)$$-optimal
5610.bi4 5610bg4 $$[1, 0, 0, -66551, 14537931]$$ $$-32597768919523300849/72509045805004050$$ $$-72509045805004050$$ $$[2]$$ $$81920$$ $$1.9239$$

## Rank

sage: E.rank()

The elliptic curves in class 5610.bi have rank $$0$$.

## Complex multiplication

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

## Modular form5610.2.a.bi

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.