# Properties

 Label 2898.j Number of curves $2$ Conductor $2898$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("j1")

sage: E.isogeny_class()

## Elliptic curves in class 2898.j

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2898.j1 2898j2 $$[1, -1, 0, -243, 6723]$$ $$-2181825073/25039686$$ $$-18253931094$$ $$$$ $$2880$$ $$0.65091$$
2898.j2 2898j1 $$[1, -1, 0, 27, -243]$$ $$2924207/34776$$ $$-25351704$$ $$[]$$ $$960$$ $$0.10160$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 2898.j have rank $$0$$.

## Complex multiplication

The elliptic curves in class 2898.j do not have complex multiplication.

## Modular form2898.2.a.j

sage: E.q_eigenform(10)

$$q - q^{2} + q^{4} + 3 q^{5} + q^{7} - q^{8} - 3 q^{10} + 5 q^{13} - q^{14} + q^{16} + 8 q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 