# Properties

 Label 63210.b Number of curves $2$ Conductor $63210$ CM no Rank $0$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 63210.b

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
63210.b1 63210b2 $$[1, 1, 0, -11638, 462988]$$ $$1481933914201/53916840$$ $$6343262309160$$ $$$$ $$207360$$ $$1.2263$$
63210.b2 63210b1 $$[1, 1, 0, -1838, -21132]$$ $$5841725401/1857600$$ $$218544782400$$ $$$$ $$103680$$ $$0.87969$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 63210.b have rank $$0$$.

## Complex multiplication

The elliptic curves in class 63210.b do not have complex multiplication.

## Modular form 63210.2.a.b

sage: E.q_eigenform(10)

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