Properties

Label 32799i
Number of curves $4$
Conductor $32799$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("i1")
 
E.isogeny_class()
 

Elliptic curves in class 32799i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
32799.d4 32799i1 \([1, 0, 0, 403, -6600]\) \(12167/39\) \(-23198109519\) \([2]\) \(22400\) \(0.67213\) \(\Gamma_0(N)\)-optimal
32799.d3 32799i2 \([1, 0, 0, -3802, -78085]\) \(10218313/1521\) \(904726271241\) \([2, 2]\) \(44800\) \(1.0187\)  
32799.d2 32799i3 \([1, 0, 0, -16417, 731798]\) \(822656953/85683\) \(50966246613243\) \([2]\) \(89600\) \(1.3653\)  
32799.d1 32799i4 \([1, 0, 0, -58467, -5446188]\) \(37159393753/1053\) \(626348957013\) \([2]\) \(89600\) \(1.3653\)  

Rank

sage: E.rank()
 

The elliptic curves in class 32799i have rank \(1\).

Complex multiplication

The elliptic curves in class 32799i do not have complex multiplication.

Modular form 32799.2.a.i

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} - q^{4} + 2 q^{5} - q^{6} - 4 q^{7} + 3 q^{8} + q^{9} - 2 q^{10} - 4 q^{11} - q^{12} + q^{13} + 4 q^{14} + 2 q^{15} - q^{16} - 2 q^{17} - q^{18} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with Cremona labels.