Properties

Label 139650.fy
Number of curves $2$
Conductor $139650$
CM no
Rank $0$
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Show commands: SageMath
sage: E = EllipticCurve("fy1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 139650.fy

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
139650.fy1 139650ek1 \([1, 1, 1, -493438, 133207031]\) \(2479176213198607/541500\) \(2902101562500\) \([2]\) \(1105920\) \(1.7751\) \(\Gamma_0(N)\)-optimal
139650.fy2 139650ek2 \([1, 1, 1, -491688, 134201031]\) \(-2452892123873647/36652781250\) \(-196435999511718750\) \([2]\) \(2211840\) \(2.1217\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 139650.2.a.fy

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.