Properties

Label 364650.d
Number of curves $4$
Conductor $364650$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("d1")
 
E.isogeny_class()
 

Elliptic curves in class 364650.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
364650.d1 364650d4 \([1, 1, 0, -221540150, -1269281301750]\) \(76959285225914579642095969/99697498164371250\) \(1557773408818300781250\) \([2]\) \(108527616\) \(3.3435\)  
364650.d2 364650d3 \([1, 1, 0, -34879650, 52529298750]\) \(300344760859819078829089/97478526510911312910\) \(1523101976732989264218750\) \([2]\) \(108527616\) \(3.3435\)  
364650.d3 364650d2 \([1, 1, 0, -13965900, -19476742500]\) \(19280154901730969757889/675674185355640900\) \(10557409146181889062500\) \([2, 2]\) \(54263808\) \(2.9970\)  
364650.d4 364650d1 \([1, 1, 0, 314600, -1069178000]\) \(220382793629361791/31740865455602160\) \(-495951022743783750000\) \([2]\) \(27131904\) \(2.6504\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 364650.d have rank \(0\).

Complex multiplication

The elliptic curves in class 364650.d do not have complex multiplication.

Modular form 364650.2.a.d

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{6} - 4 q^{7} - q^{8} + q^{9} + q^{11} - q^{12} - q^{13} + 4 q^{14} + q^{16} - q^{17} - q^{18} + 8 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.