Properties

Label 9338.b
Number of curves $2$
Conductor $9338$
CM no
Rank $2$
Graph

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

Elliptic curves in class 9338.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
9338.b1 9338a2 \([1, -1, 0, -232, 174]\) \(1384331873625/795308122\) \(795308122\) \([2]\) \(3328\) \(0.39748\)  
9338.b2 9338a1 \([1, -1, 0, 58, 0]\) \(21369234375/12456892\) \(-12456892\) \([2]\) \(1664\) \(0.050911\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 9338.b have rank \(2\).

Complex multiplication

The elliptic curves in class 9338.b do not have complex multiplication.

Modular form 9338.2.a.b

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - q^{7} - q^{8} - 3 q^{9} - 4 q^{11} - 4 q^{13} + q^{14} + q^{16} - 4 q^{17} + 3 q^{18} - 4 q^{19} + O(q^{20})\) 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.