Properties

Label 381150.gx
Number of curves $4$
Conductor $381150$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("gx1")
 
E.isogeny_class()
 

Elliptic curves in class 381150.gx

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
381150.gx1 381150gx4 \([1, -1, 0, -384771492, -2904742048334]\) \(312196988566716625/25367712678\) \(511899818288003296593750\) \([2]\) \(79626240\) \(3.5945\)  
381150.gx2 381150gx3 \([1, -1, 0, -22406742, -51844371584]\) \(-61653281712625/21875235228\) \(-441424462676600186437500\) \([2]\) \(39813120\) \(3.2480\)  
381150.gx3 381150gx2 \([1, -1, 0, -9883242, 6000585916]\) \(5290763640625/2291573592\) \(46242092073035541375000\) \([2]\) \(26542080\) \(3.0452\)  
381150.gx4 381150gx1 \([1, -1, 0, 2095758, 693888916]\) \(50447927375/39517632\) \(-797433686542647000000\) \([2]\) \(13271040\) \(2.6987\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 381150.gx have rank \(0\).

Complex multiplication

The elliptic curves in class 381150.gx do not have complex multiplication.

Modular form 381150.2.a.gx

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} + q^{7} - q^{8} + 2 q^{13} - q^{14} + q^{16} - 2 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.