Properties

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

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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)
 
\(q + 2q^{5} + q^{11} + q^{13} + q^{17} - 8q^{19} + O(q^{20})\)  Toggle raw display

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.