Properties

Label 16575.i
Number of curves $6$
Conductor $16575$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("16575.i1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 16575.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
16575.i1 16575f5 [1, 0, 1, -504351, -137883527] [2] 131072  
16575.i2 16575f3 [1, 0, 1, -34726, -1692277] [2, 2] 65536  
16575.i3 16575f2 [1, 0, 1, -13601, 589223] [2, 2] 32768  
16575.i4 16575f1 [1, 0, 1, -13476, 600973] [2] 16384 \(\Gamma_0(N)\)-optimal
16575.i5 16575f4 [1, 0, 1, 5524, 2119223] [2] 65536  
16575.i6 16575f6 [1, 0, 1, 96899, -11432527] [2] 131072  

Rank

sage: E.rank()
 

The elliptic curves in class 16575.i have rank \(0\).

Modular form 16575.2.a.i

sage: E.q_eigenform(10)
 
\( q + q^{2} + q^{3} - q^{4} + q^{6} - 3q^{8} + q^{9} + 4q^{11} - q^{12} - q^{13} - q^{16} - q^{17} + q^{18} - 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 8 & 4 \\ 2 & 1 & 2 & 4 & 4 & 2 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 8 & 4 & 2 & 1 & 4 & 8 \\ 8 & 4 & 2 & 4 & 1 & 8 \\ 4 & 2 & 4 & 8 & 8 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.