Properties

Label 166464.ec
Number of curves $4$
Conductor $166464$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("ec1")
 
E.isogeny_class()
 

Elliptic curves in class 166464.ec

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
166464.ec1 166464br3 \([0, 0, 0, -124934700, -406363348528]\) \(46753267515625/11591221248\) \(53467536436723553572749312\) \([2]\) \(31850496\) \(3.6471\)  
166464.ec2 166464br1 \([0, 0, 0, -42535020, 106734964304]\) \(1845026709625/793152\) \(3658620826272072204288\) \([2]\) \(10616832\) \(3.0978\) \(\Gamma_0(N)\)-optimal
166464.ec3 166464br2 \([0, 0, 0, -35876460, 141282237008]\) \(-1107111813625/1228691592\) \(-5667660987498723853467648\) \([2]\) \(21233664\) \(3.4443\)  
166464.ec4 166464br4 \([0, 0, 0, 301213140, -2576819527216]\) \(655215969476375/1001033261568\) \(-4617527458247276110012219392\) \([2]\) \(63700992\) \(3.9936\)  

Rank

sage: E.rank()
 

The elliptic curves in class 166464.ec have rank \(1\).

Complex multiplication

The elliptic curves in class 166464.ec do not have complex multiplication.

Modular form 166464.2.a.ec

sage: E.q_eigenform(10)
 
\(q + 2 q^{7} - 2 q^{13} - 4 q^{19} + O(q^{20})\) 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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.