Properties

Label 26950.cj
Number of curves $4$
Conductor $26950$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("cj1")
 
E.isogeny_class()
 

Elliptic curves in class 26950.cj

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
26950.cj1 26950ce4 \([1, -1, 1, -25613755, 49901510747]\) \(1010962818911303721/57392720\) \(105503064301250000\) \([2]\) \(1179648\) \(2.7331\)  
26950.cj2 26950ce3 \([1, -1, 1, -2681755, -397969253]\) \(1160306142246441/634128110000\) \(1165695906459218750000\) \([2]\) \(1179648\) \(2.7331\)  
26950.cj3 26950ce2 \([1, -1, 1, -1603755, 777050747]\) \(248158561089321/1859334400\) \(3417950512900000000\) \([2, 2]\) \(589824\) \(2.3865\)  
26950.cj4 26950ce1 \([1, -1, 1, -35755, 27546747]\) \(-2749884201/176619520\) \(-324673592320000000\) \([2]\) \(294912\) \(2.0399\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 26950.cj have rank \(1\).

Complex multiplication

The elliptic curves in class 26950.cj do not have complex multiplication.

Modular form 26950.2.a.cj

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} + q^{8} - 3 q^{9} - q^{11} - 6 q^{13} + q^{16} - 2 q^{17} - 3 q^{18} + 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.