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Properties

Label 9338b
Number of curves $2$
Conductor $9338$
CM no
Rank $0$
Graph

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

Elliptic curves in class 9338b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
9338.e2 9338b1 \([1, 1, 0, -10803361, 13736209509]\) \(-139444195316122186685933977/867810592237096964848\) \(-867810592237096964848\) \([2]\) \(727552\) \(2.8560\) \(\Gamma_0(N)\)-optimal
9338.e1 9338b2 \([1, 1, 0, -173111141, 876596829545]\) \(573718392227901342193352375257/22016176259779893044\) \(22016176259779893044\) \([2]\) \(1455104\) \(3.2025\)  

Rank

sage: E.rank()
 

The elliptic curves in class 9338b have rank \(0\).

Complex multiplication

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

Modular form 9338.2.a.b

sage: E.q_eigenform(10)
 
\(q - q^{2} + 2 q^{3} + q^{4} - 2 q^{5} - 2 q^{6} + q^{7} - q^{8} + q^{9} + 2 q^{10} + 4 q^{11} + 2 q^{12} + 2 q^{13} - q^{14} - 4 q^{15} + q^{16} - q^{18} + 2 q^{19} + O(q^{20})\) 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 Cremona 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 Cremona labels.