# Properties

 Label 5610.bh Number of curves $4$ Conductor $5610$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
E = EllipticCurve("bh1")

E.isogeny_class()

## Elliptic curves in class 5610.bh

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5610.bh1 5610bi3 $$[1, 0, 0, -19971, -1059399]$$ $$880895732965860529/26454814115400$$ $$26454814115400$$ $$$$ $$18432$$ $$1.3521$$
5610.bh2 5610bi2 $$[1, 0, 0, -2971, 38801]$$ $$2900285849172529/1019696040000$$ $$1019696040000$$ $$[2, 2]$$ $$9216$$ $$1.0055$$
5610.bh3 5610bi1 $$[1, 0, 0, -2651, 52305]$$ $$2060455000819249/517017600$$ $$517017600$$ $$$$ $$4608$$ $$0.65894$$ $$\Gamma_0(N)$$-optimal
5610.bh4 5610bi4 $$[1, 0, 0, 8909, 274025]$$ $$78200142092480591/77517928125000$$ $$-77517928125000$$ $$$$ $$18432$$ $$1.3521$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form5610.2.a.bh

sage: E.q_eigenform(10)

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

## 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. 