# Properties

 Label 114b Number of curves 2 Conductor 114 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("114.a1")
sage: E.isogeny_class()

## Elliptic curves in class 114b

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
114.a1 114b1 [1, 1, 0, -95, -399] 2 20 $$\Gamma_0(N)$$-optimal
114.a2 114b2 [1, 1, 0, -85, -473] 2 40

## Rank

sage: E.rank()

The elliptic curves in class 114b have rank $$0$$.

## Modular form114.2.a.a

sage: E.q_eigenform(10)
$$q - q^{2} - q^{3} + q^{4} + q^{6} + 4q^{7} - q^{8} + q^{9} + 4q^{11} - q^{12} - 4q^{14} + q^{16} - 2q^{17} - q^{18} + q^{19} + O(q^{20})$$

## 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. 