Properties

Label 286650.gs
Number of curves $2$
Conductor $286650$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("gs1")
 
E.isogeny_class()
 

Elliptic curves in class 286650.gs

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
286650.gs1 286650gs2 \([1, -1, 0, -12607317, -17870587659]\) \(-397052665540282969/17493884928000\) \(-9764047867392000000000\) \([]\) \(22394880\) \(2.9845\)  
286650.gs2 286650gs1 \([1, -1, 0, 788058, -68134284]\) \(96973777690391/59691453120\) \(-33316224951555000000\) \([]\) \(7464960\) \(2.4352\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 286650.gs have rank \(0\).

Complex multiplication

The elliptic curves in class 286650.gs do not have complex multiplication.

Modular form 286650.2.a.gs

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

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.