# Properties

 Label 114.b Number of curves 4 Conductor 114 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("114.b1")

sage: E.isogeny_class()

## Elliptic curves in class 114.b

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
114.b1 114c3 [1, 1, 1, -87552, -10007679]  240
114.b2 114c2 [1, 1, 1, -5472, -158079] [2, 2] 120
114.b3 114c4 [1, 1, 1, -5312, -167551]  240
114.b4 114c1 [1, 1, 1, -352, -2431]  60 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Modular form114.2.a.b

sage: E.q_eigenform(10)

$$q + q^{2} - q^{3} + q^{4} + 2q^{5} - q^{6} + q^{8} + q^{9} + 2q^{10} - 4q^{11} - q^{12} + 2q^{13} - 2q^{15} + q^{16} - 6q^{17} + q^{18} - q^{19} + O(q^{20})$$

## 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 LMFDB numbering.

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 