# Properties

 Label 546.g Number of curves $4$ Conductor $546$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
E = EllipticCurve("g1")

E.isogeny_class()

## Elliptic curves in class 546.g

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
546.g1 546g3 $$[1, 0, 0, -417, 3243]$$ $$8020417344913/187278$$ $$187278$$ $$[2]$$ $$192$$ $$0.12397$$
546.g2 546g2 $$[1, 0, 0, -27, 45]$$ $$2181825073/298116$$ $$298116$$ $$[2, 2]$$ $$96$$ $$-0.22260$$
546.g3 546g1 $$[1, 0, 0, -7, -7]$$ $$38272753/4368$$ $$4368$$ $$[2]$$ $$48$$ $$-0.56917$$ $$\Gamma_0(N)$$-optimal
546.g4 546g4 $$[1, 0, 0, 43, 255]$$ $$8780064047/32388174$$ $$-32388174$$ $$[2]$$ $$192$$ $$0.12397$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form546.2.a.g

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.