# Properties

 Label 6422.b Number of curves $2$ Conductor $6422$ CM no Rank $0$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 6422.b

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6422.b1 6422b2 $$[1, 1, 0, -11833, -553405]$$ $$-37966934881/4952198$$ $$-23903313876182$$ $$[]$$ $$23400$$ $$1.3003$$
6422.b2 6422b1 $$[1, 1, 0, -3, 2605]$$ $$-1/608$$ $$-2934699872$$ $$[]$$ $$4680$$ $$0.49554$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 6422.b have rank $$0$$.

## Complex multiplication

The elliptic curves in class 6422.b do not have complex multiplication.

## Modular form6422.2.a.b

sage: E.q_eigenform(10)

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

$$\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 