# Properties

 Label 49098e Number of curves 2 Conductor 49098 CM no Rank 2 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("49098.b1")
sage: E.isogeny_class()

## Elliptic curves in class 49098e

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
49098.b2 49098e1 [1, 1, 0, -221, 5181] 2 41472 $$\Gamma_0(N)$$-optimal
49098.b1 49098e2 [1, 1, 0, -6101, 180405] 2 82944

## Rank

sage: E.rank()

The elliptic curves in class 49098e have rank $$2$$.

## Modular form None

sage: E.q_eigenform(10)
$$q - q^{2} - q^{3} + q^{4} - 2q^{5} + q^{6} - q^{8} + q^{9} + 2q^{10} - 4q^{11} - q^{12} + 2q^{15} + q^{16} + 4q^{17} - q^{18} + 4q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.