# Properties

 Label 5610.bj Number of curves $2$ Conductor $5610$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
E = EllipticCurve("bj1")

E.isogeny_class()

## Elliptic curves in class 5610.bj

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5610.bj1 5610bh1 $$[1, 0, 0, -281, 2145]$$ $$-2454365649169/610929000$$ $$-610929000$$ $$$$ $$4752$$ $$0.40383$$ $$\Gamma_0(N)$$-optimal
5610.bj2 5610bh2 $$[1, 0, 0, 2029, -14949]$$ $$923754305147471/633316406250$$ $$-633316406250$$ $$[]$$ $$14256$$ $$0.95314$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form5610.2.a.bj

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 