# Properties

 Label 381150.pk Number of curves $4$ Conductor $381150$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("381150.pk1")

sage: E.isogeny_class()

## Elliptic curves in class 381150.pk

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
381150.pk1 381150pk3 [1, -1, 1, -2863730, 1863684397] [2] 9953280
381150.pk2 381150pk4 [1, -1, 1, -2046980, 2948328397] [2] 19906560
381150.pk3 381150pk1 [1, -1, 1, -141230, -17865603] [2] 3317760 $$\Gamma_0(N)$$-optimal
381150.pk4 381150pk2 [1, -1, 1, 221770, -94821603] [2] 6635520

## Rank

sage: E.rank()

The elliptic curves in class 381150.pk have rank $$0$$.

## Modular form 381150.2.a.pk

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} + q^{7} + q^{8} + 2q^{13} + q^{14} + q^{16} - 2q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.