# Properties

 Label 546f Number of curves $2$ Conductor $546$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("f1")

sage: E.isogeny_class()

## Elliptic curves in class 546f

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
546.f2 546f1 $$[1, 0, 0, 714, -82908]$$ $$40251338884511/2997011332224$$ $$-2997011332224$$ $$$$ $$1176$$ $$1.0736$$ $$\Gamma_0(N)$$-optimal
546.f1 546f2 $$[1, 0, 0, -3674496, -2711401518]$$ $$-5486773802537974663600129/2635437714$$ $$-2635437714$$ $$[]$$ $$8232$$ $$2.0465$$

## Rank

sage: E.rank()

The elliptic curves in class 546f have rank $$0$$.

## Complex multiplication

The elliptic curves in class 546f do not have complex multiplication.

## Modular form546.2.a.f

sage: E.q_eigenform(10)

$$q + q^{2} + q^{3} + q^{4} - q^{5} + q^{6} + q^{7} + q^{8} + q^{9} - q^{10} + 5q^{11} + q^{12} - q^{13} + q^{14} - q^{15} + q^{16} - 3q^{17} + q^{18} - q^{19} + O(q^{20})$$ ## 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 Cremona numbering.

$$\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels. 