# Properties

 Label 5610.v Number of curves $4$ Conductor $5610$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
E = EllipticCurve("v1")

E.isogeny_class()

## Elliptic curves in class 5610.v

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5610.v1 5610s3 $$[1, 0, 1, -2723, -54904]$$ $$2231707882611241/7466910$$ $$7466910$$ $$[2]$$ $$4096$$ $$0.54058$$
5610.v2 5610s4 $$[1, 0, 1, -503, 3248]$$ $$14034143923561/3445241250$$ $$3445241250$$ $$[2]$$ $$4096$$ $$0.54058$$
5610.v3 5610s2 $$[1, 0, 1, -173, -844]$$ $$567869252041/31472100$$ $$31472100$$ $$[2, 2]$$ $$2048$$ $$0.19401$$
5610.v4 5610s1 $$[1, 0, 1, 7, -52]$$ $$46268279/1211760$$ $$-1211760$$ $$[2]$$ $$1024$$ $$-0.15256$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form5610.2.a.v

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.