Properties

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

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

Elliptic curves in class 16575.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
16575.i1 16575f5 \([1, 0, 1, -504351, -137883527]\) \(908031902324522977/161726530797\) \(2526977043703125\) \([2]\) \(131072\) \(1.9599\)  
16575.i2 16575f3 \([1, 0, 1, -34726, -1692277]\) \(296380748763217/92608836489\) \(1447013070140625\) \([2, 2]\) \(65536\) \(1.6133\)  
16575.i3 16575f2 \([1, 0, 1, -13601, 589223]\) \(17806161424897/668584449\) \(10446632015625\) \([2, 2]\) \(32768\) \(1.2667\)  
16575.i4 16575f1 \([1, 0, 1, -13476, 600973]\) \(17319700013617/25857\) \(404015625\) \([2]\) \(16384\) \(0.92015\) \(\Gamma_0(N)\)-optimal
16575.i5 16575f4 \([1, 0, 1, 5524, 2119223]\) \(1193377118543/124806800313\) \(-1950106254890625\) \([2]\) \(65536\) \(1.6133\)  
16575.i6 16575f6 \([1, 0, 1, 96899, -11432527]\) \(6439735268725823/7345472585373\) \(-114773009146453125\) \([2]\) \(131072\) \(1.9599\)  

Rank

sage: E.rank()
 

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

Complex multiplication

The elliptic curves in class 16575.i do not have complex multiplication.

Modular form 16575.2.a.i

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.