Properties

 Label 350064.bx Number of curves $4$ Conductor $350064$ CM no Rank $0$ Graph

Related objects

Show commands: SageMath
sage: E = EllipticCurve("bx1")

sage: E.isogeny_class()

Elliptic curves in class 350064.bx

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
350064.bx1 350064bx4 $$[0, 0, 0, -361390052739, -83620394996644478]$$ $$1748094148784980747354970849498497/887694600425282263291392$$ $$2650641873756286033671883849728$$ $$[2]$$ $$1815478272$$ $$5.1704$$
350064.bx2 350064bx3 $$[0, 0, 0, -49435825539, 2326663485228418]$$ $$4474676144192042711273397261697/1806328356954994499451382272$$ $$5393667572613902295449836242075648$$ $$[2]$$ $$1815478272$$ $$5.1704$$
350064.bx3 350064bx2 $$[0, 0, 0, -22709056899, -1291718705683070]$$ $$433744050935826360922067531137/9612122270219882316693504$$ $$28701643304920245079529735847936$$ $$[2, 2]$$ $$907739136$$ $$4.8239$$
350064.bx4 350064bx1 $$[0, 0, 0, 128928381, -61870360369790]$$ $$79374649975090937760383/553856914190911653543936$$ $$-1653807884063435142895736193024$$ $$[2]$$ $$453869568$$ $$4.4773$$ $$\Gamma_0(N)$$-optimal

Rank

sage: E.rank()

The elliptic curves in class 350064.bx have rank $$0$$.

Complex multiplication

The elliptic curves in class 350064.bx do not have complex multiplication.

Modular form 350064.2.a.bx

sage: E.q_eigenform(10)

$$q + 2q^{5} + q^{11} + q^{13} + q^{17} - 8q^{19} + O(q^{20})$$

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.