Properties

Label 7406.e
Number of curves $2$
Conductor $7406$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("e1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 7406.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7406.e1 7406c2 \([1, 1, 0, -320320, -65460864]\) \(24553362849625/1755162752\) \(259827078332006528\) \([2]\) \(118272\) \(2.0885\)  
7406.e2 7406c1 \([1, 1, 0, 18240, -4452352]\) \(4533086375/60669952\) \(-8981330279907328\) \([2]\) \(59136\) \(1.7419\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 7406.e have rank \(0\).

Complex multiplication

The elliptic curves in class 7406.e do not have complex multiplication.

Modular form 7406.2.a.e

sage: E.q_eigenform(10)
 
\(q - q^{2} + 2q^{3} + q^{4} - 2q^{6} - q^{7} - q^{8} + q^{9} - 4q^{11} + 2q^{12} + q^{14} + q^{16} - 6q^{17} - q^{18} + 6q^{19} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.