# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("m1")

sage: E.isogeny_class()

## Elliptic curves in class 2898m

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2898.t2 2898m1 $$[1, -1, 1, -1136, -19501]$$ $$-5999796014211/2790817792$$ $$-75352080384$$ $$$$ $$5280$$ $$0.79333$$ $$\Gamma_0(N)$$-optimal
2898.t1 2898m2 $$[1, -1, 1, -100496, -12237101]$$ $$-5702623460245179/252448$$ $$-4968933984$$ $$[]$$ $$15840$$ $$1.3426$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form2898.2.a.m

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} + 3q^{5} + q^{7} + q^{8} + 3q^{10} - 6q^{11} + 5q^{13} + q^{14} + q^{16} + 6q^{17} + 2q^{19} + O(q^{20})$$ ## 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 Cremona 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 Cremona labels. 