Properties

Label 193600.hp
Number of curves $2$
Conductor $193600$
CM no
Rank $0$
Graph

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

Elliptic curves in class 193600.hp

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
193600.hp1 193600jd2 [0, -1, 0, -488033, 513139937] [] 4730880  
193600.hp2 193600jd1 [0, -1, 0, -48033, -4036063] [] 430080 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 193600.hp have rank \(0\).

Complex multiplication

The elliptic curves in class 193600.hp do not have complex multiplication.

Modular form 193600.2.a.hp

sage: E.q_eigenform(10)
 
\( q + 2q^{3} - 2q^{7} + q^{9} - q^{13} - 5q^{17} + 6q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rr} 1 & 11 \\ 11 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.