# Properties

 Label 2898.p Number of curves $2$ Conductor $2898$ CM no Rank $1$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("p1")

sage: E.isogeny_class()

## Elliptic curves in class 2898.p

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2898.p1 2898t2 $$[1, -1, 1, -5450, -143607]$$ $$24553362849625/1755162752$$ $$1279513646208$$ $$$$ $$5376$$ $$1.0701$$
2898.p2 2898t1 $$[1, -1, 1, 310, -9975]$$ $$4533086375/60669952$$ $$-44228395008$$ $$$$ $$2688$$ $$0.72349$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 2898.p have rank $$1$$.

## Complex multiplication

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

## Modular form2898.2.a.p

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} + q^{7} + q^{8} - 4q^{11} + q^{14} + q^{16} - 6q^{17} - 6q^{19} + O(q^{20})$$ ## 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. 