# Properties

 Label 158400eg Number of curves 4 Conductor 158400 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("158400.hj1")

sage: E.isogeny_class()

## Elliptic curves in class 158400eg

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
158400.hj3 158400eg1 [0, 0, 0, -11100, -434000]  262144 $$\Gamma_0(N)$$-optimal
158400.hj2 158400eg2 [0, 0, 0, -29100, 1330000] [2, 2] 524288
158400.hj1 158400eg3 [0, 0, 0, -425100, 106666000]  1048576
158400.hj4 158400eg4 [0, 0, 0, 78900, 8890000]  1048576

## Rank

sage: E.rank()

The elliptic curves in class 158400eg have rank $$1$$.

## Modular form 158400.2.a.hj

sage: E.q_eigenform(10)

$$q - q^{11} + 2q^{13} + 6q^{17} + O(q^{20})$$

## 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. 