# Properties

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

Show commands: SageMath
E = EllipticCurve("b1")

E.isogeny_class()

## Elliptic curves in class 5610.b

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5610.b1 5610d2 $$[1, 1, 0, -143, 363]$$ $$326940373369/112003650$$ $$112003650$$ $$$$ $$2048$$ $$0.24646$$
5610.b2 5610d1 $$[1, 1, 0, 27, 57]$$ $$2053225511/2098140$$ $$-2098140$$ $$$$ $$1024$$ $$-0.10012$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form5610.2.a.b

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 