Properties

Label 115920.d
Number of curves $6$
Conductor $115920$
CM no
Rank $0$
Graph

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

Elliptic curves in class 115920.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
115920.d1 115920q6 \([0, 0, 0, -12799443, -17625225742]\) \(155324313723954725282/13018359375\) \(19436306400000000\) \([2]\) \(3670016\) \(2.5680\)  
115920.d2 115920q4 \([0, 0, 0, -1101603, 444555218]\) \(198048499826486404/242568272835\) \(181076245398236160\) \([2]\) \(1835008\) \(2.2214\)  
115920.d3 115920q3 \([0, 0, 0, -801723, -274123078]\) \(76343005935514084/694180580625\) \(518203026714240000\) \([2, 2]\) \(1835008\) \(2.2214\)  
115920.d4 115920q5 \([0, 0, 0, -234723, -654353278]\) \(-957928673903042/123339801817575\) \(-184145337395224934400\) \([2]\) \(3670016\) \(2.5680\)  
115920.d5 115920q2 \([0, 0, 0, -87303, 2928998]\) \(394315384276816/208332909225\) \(38879920851206400\) \([2, 2]\) \(917504\) \(1.8748\)  
115920.d6 115920q1 \([0, 0, 0, 20742, 357527]\) \(84611246065664/53699121315\) \(-626346551018160\) \([2]\) \(458752\) \(1.5282\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 115920.d have rank \(0\).

Complex multiplication

The elliptic curves in class 115920.d do not have complex multiplication.

Modular form 115920.2.a.d

sage: E.q_eigenform(10)
 
\(q - q^{5} - q^{7} - 4q^{11} - 2q^{13} - 2q^{17} + 4q^{19} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.