Properties

Label 9408.w
Number of curves $2$
Conductor $9408$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("w1")
 
E.isogeny_class()
 

Elliptic curves in class 9408.w

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
9408.w1 9408g1 \([0, -1, 0, -408, -2862]\) \(1000000/63\) \(474360768\) \([2]\) \(3072\) \(0.41584\) \(\Gamma_0(N)\)-optimal
9408.w2 9408g2 \([0, -1, 0, 327, -12711]\) \(8000/147\) \(-70837874688\) \([2]\) \(6144\) \(0.76241\)  

Rank

sage: E.rank()
 

The elliptic curves in class 9408.w have rank \(0\).

Complex multiplication

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

Modular form 9408.2.a.w

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.