Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("hs1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 139650.hs

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
139650.hs1 139650bo2 \([1, 0, 0, -733188, 241576992]\) \(23711636464489/363888\) \(668922801750000\) \([2]\) \(1966080\) \(1.9802\)  
139650.hs2 139650bo1 \([1, 0, 0, -47188, 3534992]\) \(6321363049/715008\) \(1314374628000000\) \([2]\) \(983040\) \(1.6336\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 139650.2.a.hs

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