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Properties

Label 127050.y
Number of curves $2$
Conductor $127050$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("y1")
 
E.isogeny_class()
 

Elliptic curves in class 127050.y

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
127050.y1 127050by2 \([1, 1, 0, -2889845, -1892065875]\) \(12052620205076933/8781696\) \(1944663768432000\) \([2]\) \(3440640\) \(2.2448\)  
127050.y2 127050by1 \([1, 1, 0, -179445, -30021075]\) \(-2885728410053/79478784\) \(-17600189257728000\) \([2]\) \(1720320\) \(1.8983\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 127050.2.a.y

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{6} - q^{7} - q^{8} + q^{9} - q^{12} + 6 q^{13} + q^{14} + q^{16} + 6 q^{17} - q^{18} + 2 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.