# Properties

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

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("54150.v1")

sage: E.isogeny_class()

## Elliptic curves in class 54150q

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
54150.v2 54150q1 [1, 0, 1, -5651, -168802] [2] 92160 $$\Gamma_0(N)$$-optimal
54150.v1 54150q2 [1, 0, 1, -91151, -10599802] [2] 184320

## Rank

sage: E.rank()

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

## Modular form 54150.2.a.v

sage: E.q_eigenform(10)

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

## 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 Cremona 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 Cremona labels.