Properties

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

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("pf1")
 
E.isogeny_class()
 

Elliptic curves in class 187200.pf

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
187200.pf1 187200bx2 \([0, 0, 0, -131011500, -531840350000]\) \(666276475992821/58199166792\) \(21722722606780416000000000\) \([2]\) \(47185920\) \(3.6023\)  
187200.pf2 187200bx1 \([0, 0, 0, -128131500, -558249950000]\) \(623295446073461/5458752\) \(2037468266496000000000\) \([2]\) \(23592960\) \(3.2557\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 187200.2.a.pf

sage: E.q_eigenform(10)
 
\(q + 4 q^{7} - 2 q^{11} + q^{13} + 4 q^{17} + 2 q^{19} + O(q^{20})\) 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 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.