Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("d1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 7406.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7406.d1 7406b2 \([1, -1, 0, -126001, -17129673]\) \(1494447319737/5411854\) \(801148618028206\) \([2]\) \(50688\) \(1.7208\)  
7406.d2 7406b1 \([1, -1, 0, -4331, -509551]\) \(-60698457/725788\) \(-107442671805532\) \([2]\) \(25344\) \(1.3742\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 7406.2.a.d

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} + 2 q^{5} - q^{7} - q^{8} - 3 q^{9} - 2 q^{10} + 4 q^{11} + 4 q^{13} + q^{14} + q^{16} + 8 q^{17} + 3 q^{18} + 2 q^{19} + O(q^{20})\)  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.