# Properties

 Label 162.b Number of curves $4$ Conductor $162$ CM no Rank $0$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 162.b

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
162.b1 162c3 $$[1, -1, 0, -1077, 13877]$$ $$-189613868625/128$$ $$-93312$$ $$$$ $$42$$ $$0.26937$$
162.b2 162c4 $$[1, -1, 0, -852, 19664]$$ $$-1159088625/2097152$$ $$-123834728448$$ $$[]$$ $$126$$ $$0.81867$$
162.b3 162c2 $$[1, -1, 0, -42, -100]$$ $$-140625/8$$ $$-472392$$ $$[]$$ $$18$$ $$-0.15428$$
162.b4 162c1 $$[1, -1, 0, 3, -1]$$ $$3375/2$$ $$-1458$$ $$$$ $$6$$ $$-0.70359$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 162.b have rank $$0$$.

## Complex multiplication

The elliptic curves in class 162.b do not have complex multiplication.

## Modular form162.2.a.b

sage: E.q_eigenform(10)

$$q - q^{2} + q^{4} + 2q^{7} - q^{8} + 3q^{11} + 2q^{13} - 2q^{14} + q^{16} + 3q^{17} - q^{19} + O(q^{20})$$ ## 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.

$$\left(\begin{array}{rrrr} 1 & 3 & 21 & 7 \\ 3 & 1 & 7 & 21 \\ 21 & 7 & 1 & 3 \\ 7 & 21 & 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 