# Properties

 Label 24150.y Number of curves $6$ Conductor $24150$ CM no Rank $1$ Graph

# Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("24150.y1")

sage: E.isogeny_class()

## Elliptic curves in class 24150.y

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
24150.y1 24150bc6 [1, 0, 1, -1978351, -1071187402] [2] 524288
24150.y2 24150bc4 [1, 0, 1, -442851, 113391598] [2] 262144
24150.y3 24150bc3 [1, 0, 1, -126851, -15832402] [2, 2] 262144
24150.y4 24150bc2 [1, 0, 1, -28851, 1611598] [2, 2] 131072
24150.y5 24150bc1 [1, 0, 1, 3149, 139598] [2] 65536 $$\Gamma_0(N)$$-optimal
24150.y6 24150bc5 [1, 0, 1, 156649, -76501402] [2] 524288

## Rank

sage: E.rank()

The elliptic curves in class 24150.y have rank $$1$$.

## Modular form 24150.2.a.y

sage: E.q_eigenform(10)

$$q - q^{2} + q^{3} + q^{4} - q^{6} - q^{7} - q^{8} + q^{9} - 4q^{11} + q^{12} + 2q^{13} + q^{14} + q^{16} + 6q^{17} - q^{18} + 4q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrrrr} 1 & 8 & 2 & 4 & 8 & 4 \\ 8 & 1 & 4 & 2 & 4 & 8 \\ 2 & 4 & 1 & 2 & 4 & 2 \\ 4 & 2 & 2 & 1 & 2 & 4 \\ 8 & 4 & 4 & 2 & 1 & 8 \\ 4 & 8 & 2 & 4 & 8 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.