Properties

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

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Show commands: SageMath
E = EllipticCurve("bm1")
 
E.isogeny_class()
 

Elliptic curves in class 9408.bm

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
9408.bm1 9408cg2 \([0, -1, 0, -2231329, -1288709183]\) \(-16591834777/98304\) \(-7279331738306740224\) \([]\) \(241920\) \(2.4596\)  
9408.bm2 9408cg1 \([0, -1, 0, 73631, -9456383]\) \(596183/864\) \(-63978501606211584\) \([]\) \(80640\) \(1.9103\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

The elliptic curves in class 9408.bm do not have complex multiplication.

Modular form 9408.2.a.bm

sage: E.q_eigenform(10)
 
\(q - q^{3} + 3 q^{5} + q^{9} + 3 q^{11} - 4 q^{13} - 3 q^{15} + 4 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.