Properties

Label 139650.gi
Number of curves $2$
Conductor $139650$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("gi1")
 
E.isogeny_class()
 

Elliptic curves in class 139650.gi

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
139650.gi1 139650er2 \([1, 1, 1, -2448188, 1470250781]\) \(882774443450089/2166000000\) \(3981683343750000000\) \([2]\) \(5806080\) \(2.4472\)  
139650.gi2 139650er1 \([1, 1, 1, -96188, 40234781]\) \(-53540005609/350208000\) \(-643775328000000000\) \([2]\) \(2903040\) \(2.1006\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 139650.gi have rank \(1\).

Complex multiplication

The elliptic curves in class 139650.gi do not have complex multiplication.

Modular form 139650.2.a.gi

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} - q^{6} + q^{8} + q^{9} + 4 q^{11} - q^{12} - 6 q^{13} + q^{16} + 4 q^{17} + q^{18} - q^{19} + O(q^{20})\) 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.