Properties

Label 26775.n
Number of curves 4
Conductor 26775
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("26775.n1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 26775.n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
26775.n1 26775x4 [1, -1, 1, -379355, -89833728] [2] 196608  
26775.n2 26775x3 [1, -1, 1, -120605, 15016272] [2] 196608  
26775.n3 26775x2 [1, -1, 1, -24980, -1239978] [2, 2] 98304  
26775.n4 26775x1 [1, -1, 1, 3145, -114978] [2] 49152 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 26775.n have rank \(0\).

Modular form 26775.2.a.n

sage: E.q_eigenform(10)
 
\( q - q^{2} - q^{4} - q^{7} + 3q^{8} + 6q^{13} + q^{14} - q^{16} - q^{17} + 4q^{19} + O(q^{20}) \)

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.