Properties

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

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Show commands: SageMath
E = EllipticCurve("b1")
 
E.isogeny_class()
 

Elliptic curves in class 9408.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
9408.b1 9408ch2 \([0, -1, 0, -431265, 106164801]\) \(838561807/26244\) \(277620998041239552\) \([2]\) \(172032\) \(2.1222\)  
9408.b2 9408ch1 \([0, -1, 0, 7775, 5624641]\) \(4913/1296\) \(-13709678915616768\) \([2]\) \(86016\) \(1.7756\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 9408.2.a.b

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.