Properties

Label 9408.cb
Number of curves $4$
Conductor $9408$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("cb1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 9408.cb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
9408.cb1 9408da3 \([0, 1, 0, -43969, 3534047]\) \(2438569736/21\) \(80957571072\) \([2]\) \(24576\) \(1.2609\)  
9408.cb2 9408da2 \([0, 1, 0, -2809, 51911]\) \(5088448/441\) \(212513624064\) \([2, 2]\) \(12288\) \(0.91432\)  
9408.cb3 9408da1 \([0, 1, 0, -604, -4978]\) \(3241792/567\) \(4269246912\) \([2]\) \(6144\) \(0.56775\) \(\Gamma_0(N)\)-optimal
9408.cb4 9408da4 \([0, 1, 0, 3071, 245951]\) \(830584/7203\) \(-27768446877696\) \([2]\) \(24576\) \(1.2609\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 9408.2.a.cb

sage: E.q_eigenform(10)
 
\(q + q^{3} - 2 q^{5} + q^{9} + 4 q^{11} - 6 q^{13} - 2 q^{15} + 2 q^{17} + 4 q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.