Properties

Label 26640.x
Number of curves $4$
Conductor $26640$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("x1")
 
E.isogeny_class()
 

Elliptic curves in class 26640.x

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
26640.x1 26640bk4 \([0, 0, 0, -1510203, -318864022]\) \(127568139540190201/59114336463360\) \(176514462850209546240\) \([2]\) \(1161216\) \(2.5796\)  
26640.x2 26640bk2 \([0, 0, 0, -765003, 257525498]\) \(16581570075765001/998001000\) \(2980015017984000\) \([2]\) \(387072\) \(2.0303\)  
26640.x3 26640bk1 \([0, 0, 0, -45003, 4517498]\) \(-3375675045001/999000000\) \(-2982998016000000\) \([2]\) \(193536\) \(1.6837\) \(\Gamma_0(N)\)-optimal
26640.x4 26640bk3 \([0, 0, 0, 332997, -37591702]\) \(1367594037332999/995878502400\) \(-2973677274110361600\) \([2]\) \(580608\) \(2.2330\)  

Rank

sage: E.rank()
 

The elliptic curves in class 26640.x have rank \(0\).

Complex multiplication

The elliptic curves in class 26640.x do not have complex multiplication.

Modular form 26640.2.a.x

sage: E.q_eigenform(10)
 
\(q - q^{5} + 4 q^{7} + 6 q^{11} + 2 q^{13} + 6 q^{17} - 2 q^{19} + O(q^{20})\) 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 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.