Properties

Label 9338h
Number of curves $4$
Conductor $9338$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("h1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 9338h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
9338.i4 9338h1 \([1, -1, 1, -45019, 3721611]\) \(-10090256344188054273/107965577101312\) \(-107965577101312\) \([4]\) \(38400\) \(1.5091\) \(\Gamma_0(N)\)-optimal
9338.i3 9338h2 \([1, -1, 1, -722139, 236380043]\) \(41647175116728660507393/4693358285056\) \(4693358285056\) \([2, 2]\) \(76800\) \(1.8556\)  
9338.i2 9338h3 \([1, -1, 1, -723979, 235116331]\) \(41966336340198080824833/442001722607124848\) \(442001722607124848\) \([2]\) \(153600\) \(2.2022\)  
9338.i1 9338h4 \([1, -1, 1, -11554219, 15119657963]\) \(170586815436843383543017473/2166416\) \(2166416\) \([2]\) \(153600\) \(2.2022\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 9338.2.a.h

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} + 2q^{5} - q^{7} + q^{8} - 3q^{9} + 2q^{10} + 4q^{11} + 6q^{13} - q^{14} + q^{16} + 6q^{17} - 3q^{18} + 4q^{19} + O(q^{20})\)  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 Cremona 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 Cremona labels.