Properties

Label 115920.g
Number of curves $4$
Conductor $115920$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("g1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 115920.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
115920.g1 115920p4 \([0, 0, 0, -1669323, -830154022]\) \(344577854816148242/2716875\) \(4056272640000\) \([2]\) \(983040\) \(2.0102\)  
115920.g2 115920p2 \([0, 0, 0, -104403, -12952798]\) \(168591300897604/472410225\) \(352652343321600\) \([2, 2]\) \(491520\) \(1.6636\)  
115920.g3 115920p3 \([0, 0, 0, -63003, -23327638]\) \(-18524646126002/146738831715\) \(-219079901839841280\) \([2]\) \(983040\) \(2.0102\)  
115920.g4 115920p1 \([0, 0, 0, -9183, -21922]\) \(458891455696/264449745\) \(49352669210880\) \([2]\) \(245760\) \(1.3171\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 115920.2.a.g

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.