# Properties

 Label 4650.bu Number of curves $2$ Conductor $4650$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
E = EllipticCurve("bu1")

E.isogeny_class()

## Elliptic curves in class 4650.bu

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4650.bu1 4650bp2 $$[1, 0, 0, -59388, -8815608]$$ $$-2372030262025/2061298872$$ $$-20129871796875000$$ $$[]$$ $$36000$$ $$1.8258$$
4650.bu2 4650bp1 $$[1, 0, 0, -1428, 62352]$$ $$-12882119799145/59982446592$$ $$-1499561164800$$ $$$$ $$7200$$ $$1.0210$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 4650.bu have rank $$0$$.

## Complex multiplication

The elliptic curves in class 4650.bu do not have complex multiplication.

## Modular form4650.2.a.bu

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 