Properties

Label 116886.w
Number of curves $4$
Conductor $116886$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("w1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 116886.w

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
116886.w1 116886p4 \([1, 0, 1, -833935, 293040218]\) \(36204575259448513/1527466248\) \(2705999633773128\) \([2]\) \(1658880\) \(2.0413\)  
116886.w2 116886p2 \([1, 0, 1, -54695, 4098026]\) \(10214075575873/1806590016\) \(3200484415334976\) \([2, 2]\) \(829440\) \(1.6947\)  
116886.w3 116886p1 \([1, 0, 1, -15975, -718742]\) \(254478514753/21762048\) \(38552795516928\) \([2]\) \(414720\) \(1.3481\) \(\Gamma_0(N)\)-optimal
116886.w4 116886p3 \([1, 0, 1, 105025, 23583866]\) \(72318867421247/177381135624\) \(-314241502007189064\) \([2]\) \(1658880\) \(2.0413\)  

Rank

sage: E.rank()
 

The elliptic curves in class 116886.w have rank \(0\).

Complex multiplication

The elliptic curves in class 116886.w do not have complex multiplication.

Modular form 116886.2.a.w

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} + 2q^{5} - q^{6} - q^{7} - q^{8} + q^{9} - 2q^{10} + q^{12} - 2q^{13} + q^{14} + 2q^{15} + q^{16} - 2q^{17} - q^{18} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.