# Properties

 Label 705600.bub Number of curves $4$ Conductor $705600$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("bub1")

sage: E.isogeny_class()

## Elliptic curves in class 705600.bub

sage: E.isogeny_class().curves

LMFDB label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height
705600.bub1 $$[0, 0, 0, -49406700, 133667786000]$$ $$303735479048/105$$ $$4610786664960000000$$ $$$$ $$56623104$$ $$2.9371$$
705600.bub2 $$[0, 0, 0, -3101700, 2068976000]$$ $$601211584/11025$$ $$60516574977600000000$$ $$[2, 2]$$ $$28311552$$ $$2.5906$$
705600.bub3 $$[0, 0, 0, -400575, -48706000]$$ $$82881856/36015$$ $$3088866847815000000$$ $$$$ $$14155776$$ $$2.2440$$
705600.bub4 $$[0, 0, 0, -14700, 6001814000]$$ $$-8/354375$$ $$-15561404994240000000000$$ $$$$ $$56623104$$ $$2.9371$$

## Rank

sage: E.rank()

The elliptic curves in class 705600.bub have rank $$0$$.

## Complex multiplication

The elliptic curves in class 705600.bub do not have complex multiplication.

## Modular form 705600.2.a.bub

sage: E.q_eigenform(10)

$$q + 4q^{11} - 6q^{13} + 6q^{17} + 4q^{19} + O(q^{20})$$ ## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 