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Properties

Label 127050.gx
Number of curves $4$
Conductor $127050$
CM no
Rank $1$
Graph

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

Elliptic curves in class 127050.gx

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
127050.gx1 127050gy4 \([1, 1, 1, -20130703513, -1099328827258969]\) \(260744057755293612689909/8504954620259328\) \(29427824046916475334000000000\) \([2]\) \(230400000\) \(4.5567\)  
127050.gx2 127050gy3 \([1, 1, 1, -1312783513, -15604814458969]\) \(72313087342699809269/11447096545640448\) \(39607870709944018944000000000\) \([2]\) \(115200000\) \(4.2101\)  
127050.gx3 127050gy2 \([1, 1, 1, -356202888, 2563721984781]\) \(1444540994277943589/15251205665388\) \(52770392890196153648437500\) \([2]\) \(46080000\) \(3.7519\)  
127050.gx4 127050gy1 \([1, 1, 1, -355295388, 2577552284781]\) \(1433528304665250149/162339408\) \(561707351515406250000\) \([2]\) \(23040000\) \(3.4054\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 127050.gx have rank \(1\).

Complex multiplication

The elliptic curves in class 127050.gx do not have complex multiplication.

Modular form 127050.2.a.gx

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

\(\left(\begin{array}{rrrr} 1 & 2 & 5 & 10 \\ 2 & 1 & 10 & 5 \\ 5 & 10 & 1 & 2 \\ 10 & 5 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.