# Properties

 Label 462.b Number of curves $2$ Conductor $462$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
E = EllipticCurve("b1")

E.isogeny_class()

## Elliptic curves in class 462.b

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
462.b1 462a2 $$[1, 1, 0, -105, -441]$$ $$129938649625/7072758$$ $$7072758$$ $$$$ $$128$$ $$0.070209$$
462.b2 462a1 $$[1, 1, 0, 5, -23]$$ $$9938375/274428$$ $$-274428$$ $$$$ $$64$$ $$-0.27636$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 462.b have rank $$1$$.

## Complex multiplication

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

## Modular form462.2.a.b

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 