# Properties

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

# Related objects

Show commands: SageMath
E = EllipticCurve("w1")

E.isogeny_class()

## Elliptic curves in class 5610.w

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5610.w1 5610z1 $$[1, 1, 1, -1024276, -399370027]$$ $$118843307222596927933249/19794099600000000$$ $$19794099600000000$$ $$[2]$$ $$134400$$ $$2.1348$$ $$\Gamma_0(N)$$-optimal
5610.w2 5610z2 $$[1, 1, 1, -924276, -480330027]$$ $$-87323024620536113533249/48975797371840020000$$ $$-48975797371840020000$$ $$[2]$$ $$268800$$ $$2.4814$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form5610.2.a.w

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.