# Properties

 Label 54150.ch Number of curves $2$ Conductor $54150$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("54150.ch1")

sage: E.isogeny_class()

## Elliptic curves in class 54150.ch

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
54150.ch1 54150br2 [1, 1, 1, -667088, -209456719] [2] 1474560
54150.ch2 54150br1 [1, 1, 1, -59088, -304719] [2] 737280 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 54150.ch have rank $$0$$.

## Modular form 54150.2.a.ch

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.