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Properties

Label 9338.d
Number of curves $2$
Conductor $9338$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("d1")
 
E.isogeny_class()
 

Elliptic curves in class 9338.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
9338.d1 9338d2 \([1, -1, 0, -825301, 288786717]\) \(62167173500157644301993/7582456\) \(7582456\) \([2]\) \(55296\) \(1.6541\)  
9338.d2 9338d1 \([1, -1, 0, -51581, 4521989]\) \(-15177411906818559273/167619938752\) \(-167619938752\) \([2]\) \(27648\) \(1.3076\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 9338.d have rank \(1\).

Complex multiplication

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

Modular form 9338.2.a.d

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