# Properties

 Label 54150.v Number of curves $2$ Conductor $54150$ CM no Rank $0$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 54150.v

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
54150.v1 54150q2 $$[1, 0, 1, -91151, -10599802]$$ $$781484460931/900$$ $$96454687500$$ $$$$ $$184320$$ $$1.3917$$
54150.v2 54150q1 $$[1, 0, 1, -5651, -168802]$$ $$-186169411/6480$$ $$-694473750000$$ $$$$ $$92160$$ $$1.0451$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

The elliptic curves in class 54150.v do not have complex multiplication.

## 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 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. 