# Properties

 Label 150.b Number of curves 8 Conductor 150 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("150.b1")

sage: E.isogeny_class()

## Elliptic curves in class 150.b

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
150.b1 150c7 [1, 1, 1, -133338, -18795969] [2] 576
150.b2 150c8 [1, 1, 1, -11338, -67969] [2] 576
150.b3 150c6 [1, 1, 1, -8338, -295969] [2, 2] 288
150.b4 150c5 [1, 1, 1, -7213, 232781] [2] 192
150.b5 150c4 [1, 1, 1, -1713, -24219] [2] 192
150.b6 150c2 [1, 1, 1, -463, 3281] [2, 2] 96
150.b7 150c3 [1, 1, 1, -338, -7969] [4] 144
150.b8 150c1 [1, 1, 1, 37, 281] [4] 48 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 150.b have rank $$0$$.

## Modular form150.2.a.b

sage: E.q_eigenform(10)

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

## 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 LMFDB numbering.

$$\left(\begin{array}{rrrrrrrr} 1 & 4 & 2 & 12 & 3 & 6 & 4 & 12 \\ 4 & 1 & 2 & 3 & 12 & 6 & 4 & 12 \\ 2 & 2 & 1 & 6 & 6 & 3 & 2 & 6 \\ 12 & 3 & 6 & 1 & 4 & 2 & 12 & 4 \\ 3 & 12 & 6 & 4 & 1 & 2 & 12 & 4 \\ 6 & 6 & 3 & 2 & 2 & 1 & 6 & 2 \\ 4 & 4 & 2 & 12 & 12 & 6 & 1 & 3 \\ 12 & 12 & 6 & 4 & 4 & 2 & 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.