Properties

Label 466752ba
Number of curves $4$
Conductor $466752$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("ba1")
 
E.isogeny_class()
 

Elliptic curves in class 466752ba

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
466752.ba3 466752ba1 \([0, -1, 0, -6420833, 4057229793]\) \(111675519439697265625/37528570137307392\) \(9837889490074308968448\) \([2]\) \(29196288\) \(2.9225\) \(\Gamma_0(N)\)-optimal
466752.ba4 466752ba2 \([0, -1, 0, 18733727, 28019463649]\) \(2773679829880629422375/2899504554614368272\) \(-760087721964828956295168\) \([2]\) \(58392576\) \(3.2691\)  
466752.ba1 466752ba3 \([0, -1, 0, -210894113, -1178543587935]\) \(3957101249824708884951625/772310238681366528\) \(202456495208888147116032\) \([2]\) \(87588864\) \(3.4718\)  
466752.ba2 466752ba4 \([0, -1, 0, -188611873, -1437325066847]\) \(-2830680648734534916567625/1766676274677722124288\) \(-463123585349116788549353472\) \([2]\) \(175177728\) \(3.8184\)  

Rank

sage: E.rank()
 

The elliptic curves in class 466752ba have rank \(0\).

Complex multiplication

The elliptic curves in class 466752ba do not have complex multiplication.

Modular form 466752.2.a.ba

sage: E.q_eigenform(10)
 
\(q - q^{3} - 4 q^{7} + q^{9} - q^{11} - q^{13} + q^{17} - 2 q^{19} + O(q^{20})\) Copy content 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 Cremona numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.