Properties

Label 38808.n
Number of curves $2$
Conductor $38808$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("n1")
 
E.isogeny_class()
 

Elliptic curves in class 38808.n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
38808.n1 38808g2 \([0, 0, 0, -40131, 2991646]\) \(3203226/121\) \(269998559373312\) \([2]\) \(129024\) \(1.5375\)  
38808.n2 38808g1 \([0, 0, 0, 1029, 168070]\) \(108/11\) \(-12272661789696\) \([2]\) \(64512\) \(1.1910\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 38808.n have rank \(0\).

Complex multiplication

The elliptic curves in class 38808.n do not have complex multiplication.

Modular form 38808.2.a.n

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