Properties

Label 139650.ij
Number of curves $2$
Conductor $139650$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("ij1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 139650.ij

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
139650.ij1 139650by1 \([1, 0, 0, -547478, -213208668]\) \(-2569823930905/1292464512\) \(-9127230871271587200\) \([]\) \(3048192\) \(2.3431\) \(\Gamma_0(N)\)-optimal
139650.ij2 139650by2 \([1, 0, 0, 4314547, 2673861777]\) \(1257792236741495/1165133611008\) \(-8228035172193848524800\) \([]\) \(9144576\) \(2.8924\)  

Rank

sage: E.rank()
 

The elliptic curves in class 139650.ij have rank \(0\).

Complex multiplication

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

Modular form 139650.2.a.ij

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} + q^{6} + q^{8} + q^{9} + q^{12} + 5q^{13} + q^{16} + 6q^{17} + q^{18} - q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.