Properties

Label 116550ep
Number of curves $4$
Conductor $116550$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("ep1")
 
E.isogeny_class()
 

Elliptic curves in class 116550ep

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
116550.fe4 116550ep1 \([1, -1, 1, 17995, -760003]\) \(56578878719/54390000\) \(-619536093750000\) \([2]\) \(491520\) \(1.5254\) \(\Gamma_0(N)\)-optimal
116550.fe3 116550ep2 \([1, -1, 1, -94505, -6835003]\) \(8194759433281/2958272100\) \(33696568139062500\) \([2, 2]\) \(983040\) \(1.8720\)  
116550.fe2 116550ep3 \([1, -1, 1, -645755, 194922497]\) \(2614441086442081/74385450090\) \(847296767431406250\) \([2]\) \(1966080\) \(2.2186\)  
116550.fe1 116550ep4 \([1, -1, 1, -1343255, -598742503]\) \(23531588875176481/6398929110\) \(72887801893593750\) \([2]\) \(1966080\) \(2.2186\)  

Rank

sage: E.rank()
 

The elliptic curves in class 116550ep have rank \(0\).

Complex multiplication

The elliptic curves in class 116550ep do not have complex multiplication.

Modular form 116550.2.a.ep

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} + q^{7} + q^{8} + 2 q^{13} + q^{14} + q^{16} + 2 q^{17} + O(q^{20})\) 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.