# Properties

 Label 116b Number of curves 2 Conductor 116 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("116.b1")
sage: E.isogeny_class()

## Elliptic curves in class 116b

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
116.b1 116b1 [0, 1, 0, -4, 4] 3 8 $$\Gamma_0(N)$$-optimal
116.b2 116b2 [0, 1, 0, 36, -76] 1 24

## Rank

sage: E.rank()

The elliptic curves in class 116b have rank $$0$$.

## Modular form116.2.a.b

sage: E.q_eigenform(10)
$$q + q^{3} + 3q^{5} - 4q^{7} - 2q^{9} + 3q^{11} + 5q^{13} + 3q^{15} - 6q^{17} - 4q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels. 