# Properties

 Label 462.g Number of curves $4$ Conductor $462$ CM no Rank $0$ Graph

# Related objects

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

E.isogeny_class()

## Elliptic curves in class 462.g

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
462.g1 462f4 $$[1, 0, 0, -40247, 3104415]$$ $$7209828390823479793/49509306$$ $$49509306$$ $$[2]$$ $$768$$ $$1.0762$$
462.g2 462f3 $$[1, 0, 0, -3507, 6507]$$ $$4770223741048753/2740574865798$$ $$2740574865798$$ $$[2]$$ $$768$$ $$1.0762$$
462.g3 462f2 $$[1, 0, 0, -2517, 48285]$$ $$1763535241378513/4612311396$$ $$4612311396$$ $$[2, 2]$$ $$384$$ $$0.72966$$
462.g4 462f1 $$[1, 0, 0, -97, 1337]$$ $$-100999381393/723148272$$ $$-723148272$$ $$[4]$$ $$192$$ $$0.38308$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 462.g have rank $$0$$.

## Complex multiplication

The elliptic curves in class 462.g do not have complex multiplication.

## Modular form462.2.a.g

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.