# Properties

 Label 546.d Number of curves $3$ Conductor $546$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("d1")

sage: E.isogeny_class()

## Elliptic curves in class 546.d

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
546.d1 546d3 $$[1, 0, 1, -26057, -1621108]$$ $$-1956469094246217097/36641439744$$ $$-36641439744$$ $$[]$$ $$1944$$ $$1.1515$$
546.d2 546d2 $$[1, 0, 1, -122, -4948]$$ $$-198461344537/10417365504$$ $$-10417365504$$ $$[3]$$ $$648$$ $$0.60215$$
546.d3 546d1 $$[1, 0, 1, 13, 182]$$ $$270840023/14329224$$ $$-14329224$$ $$[3]$$ $$216$$ $$0.052847$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form546.2.a.d

sage: E.q_eigenform(10)

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

## 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 LMFDB numbering.

$$\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.