# Properties

 Label 259182.fu Number of curves $4$ Conductor $259182$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("fu1")

sage: E.isogeny_class()

## Elliptic curves in class 259182.fu

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
259182.fu1 259182fu3 $$[1, -1, 1, -5531054, 5008177221]$$ $$14489843500598257/6246072$$ $$8066601920067768$$ $$[2]$$ $$8847360$$ $$2.3948$$
259182.fu2 259182fu4 $$[1, -1, 1, -739454, -129184635]$$ $$34623662831857/14438442312$$ $$18646785768202304328$$ $$[2]$$ $$8847360$$ $$2.3948$$
259182.fu3 259182fu2 $$[1, -1, 1, -347414, 77498853]$$ $$3590714269297/73410624$$ $$94807469480302656$$ $$[2, 2]$$ $$4423680$$ $$2.0482$$
259182.fu4 259182fu1 $$[1, -1, 1, 1066, 3621093]$$ $$103823/4386816$$ $$-5665432349896704$$ $$[2]$$ $$2211840$$ $$1.7017$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 259182.fu have rank $$0$$.

## Complex multiplication

The elliptic curves in class 259182.fu do not have complex multiplication.

## Modular form 259182.2.a.fu

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} + 2q^{5} + q^{7} + q^{8} + 2q^{10} + 6q^{13} + q^{14} + q^{16} + q^{17} + O(q^{20})$$

## 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.