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Properties

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

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Show commands: SageMath
E = EllipticCurve("v1")
 
E.isogeny_class()
 

Elliptic curves in class 127050.v

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
127050.v1 127050bx2 \([1, 1, 0, -202435, 29559325]\) \(4143026834981/683305392\) \(151314647944614000\) \([2]\) \(2211840\) \(2.0180\)  
127050.v2 127050bx1 \([1, 1, 0, -57235, -4853075]\) \(93638512421/8692992\) \(1925020700064000\) \([2]\) \(1105920\) \(1.6715\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 127050.2.a.v

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