# Properties

 Label 5610.m Number of curves $2$ Conductor $5610$ CM no Rank $1$ Graph

# Related objects

Show commands: SageMath
E = EllipticCurve("m1")

E.isogeny_class()

## Elliptic curves in class 5610.m

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5610.m1 5610k1 $$[1, 0, 1, -8504, 301106]$$ $$68001744211490809/1022422500$$ $$1022422500$$ $$[2]$$ $$8064$$ $$0.86538$$ $$\Gamma_0(N)$$-optimal
5610.m2 5610k2 $$[1, 0, 1, -8254, 319706]$$ $$-62178675647294809/8362782148050$$ $$-8362782148050$$ $$[2]$$ $$16128$$ $$1.2120$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form5610.2.a.m

sage: E.q_eigenform(10)

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

## 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.