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Properties

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

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Show commands: SageMath
E = EllipticCurve("hp1")
 
E.isogeny_class()
 

Elliptic curves in class 139650hp

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
139650.k2 139650hp1 \([1, 1, 0, -193575, -34252875]\) \(-3491055413/175104\) \(-40235958000000000\) \([2]\) \(1843200\) \(1.9470\) \(\Gamma_0(N)\)-optimal
139650.k1 139650hp2 \([1, 1, 0, -3133575, -2136352875]\) \(14809006736693/34656\) \(7963366687500000\) \([2]\) \(3686400\) \(2.2936\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 139650.2.a.hp

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