# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("r1")

sage: E.isogeny_class()

## Elliptic curves in class 2898.r

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2898.r1 2898o2 $$[1, -1, 1, -30119, -1750017]$$ $$4144806984356137/568114785504$$ $$414155678632416$$ $$$$ $$15360$$ $$1.5316$$
2898.r2 2898o1 $$[1, -1, 1, 3001, -147009]$$ $$4101378352343/15049939968$$ $$-10971406236672$$ $$$$ $$7680$$ $$1.1851$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form2898.2.a.r

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} + 2 q^{5} - q^{7} + q^{8} + 2 q^{10} + 4 q^{13} - q^{14} + q^{16} + 6 q^{19} + O(q^{20})$$ ## 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. 