Properties

Label 9408.k
Number of curves $2$
Conductor $9408$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("9408.k1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 9408.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
9408.k1 9408cc2 [0, -1, 0, -3649, -83705] [] 6240  
9408.k2 9408cc1 [0, -1, 0, -9, 15] [] 480 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 9408.k have rank \(1\).

Modular form 9408.2.a.k

sage: E.q_eigenform(10)
 
\( q - q^{3} - 2q^{5} + q^{9} - 2q^{11} + q^{13} + 2q^{15} - q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rr} 1 & 13 \\ 13 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.