# Properties

 Label 158400kh Number of curves 4 Conductor 158400 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("158400.y1")

sage: E.isogeny_class()

## Elliptic curves in class 158400kh

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
158400.y4 158400kh1 [0, 0, 0, 600, -155000]  393216 $$\Gamma_0(N)$$-optimal
158400.y3 158400kh2 [0, 0, 0, -39900, -2990000] [2, 2] 786432
158400.y2 158400kh3 [0, 0, 0, -93900, 6838000]  1572864
158400.y1 158400kh4 [0, 0, 0, -633900, -194258000]  1572864

## Rank

sage: E.rank()

The elliptic curves in class 158400kh have rank $$0$$.

## Modular form 158400.2.a.y

sage: E.q_eigenform(10)

$$q - 4q^{7} - q^{11} + 6q^{13} + 6q^{17} + 8q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels. 