Properties

Label 187200.pe
Number of curves $2$
Conductor $187200$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("pe1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 187200.pe

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
187200.pe1 187200bw2 \([0, 0, 0, -8940, 106000]\) \(26463592/13689\) \(40875134976000\) \([2]\) \(458752\) \(1.3038\)  
187200.pe2 187200bw1 \([0, 0, 0, -7140, 232000]\) \(107850176/117\) \(43670016000\) \([2]\) \(229376\) \(0.95725\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 187200.pe have rank \(1\).

Complex multiplication

The elliptic curves in class 187200.pe do not have complex multiplication.

Modular form 187200.2.a.pe

sage: E.q_eigenform(10)
 
\(q + 4q^{7} - 2q^{11} + q^{13} - 2q^{19} + O(q^{20})\)  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.