# Properties

 Label 116281b Number of curves $2$ Conductor $116281$ CM no Rank $1$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 116281b

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
116281.c2 116281b1 [1, 0, 1, -2423, 179199] [] 183600 $$\Gamma_0(N)$$-optimal
116281.c1 116281b2 [1, 0, 1, -3490853, -2510792715] [] 2019600

## Rank

sage: E.rank()

The elliptic curves in class 116281b have rank $$1$$.

## Complex multiplication

The elliptic curves in class 116281b do not have complex multiplication.

## Modular form 116281.2.a.b

sage: E.q_eigenform(10)

$$q + q^{2} - 2q^{3} - q^{4} + q^{5} - 2q^{6} - 2q^{7} - 3q^{8} + q^{9} + q^{10} + 2q^{12} - q^{13} - 2q^{14} - 2q^{15} - q^{16} + 5q^{17} + q^{18} + 6q^{19} + O(q^{20})$$

## 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 Cremona numbering.

$$\left(\begin{array}{rr} 1 & 11 \\ 11 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels. 