Properties

Label 187200.pt
Number of curves $2$
Conductor $187200$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("pt1")
 
E.isogeny_class()
 

Elliptic curves in class 187200.pt

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
187200.pt1 187200cc2 \([0, 0, 0, -223500, -13250000]\) \(26463592/13689\) \(638673984000000000\) \([2]\) \(2293760\) \(2.1085\)  
187200.pt2 187200cc1 \([0, 0, 0, -178500, -29000000]\) \(107850176/117\) \(682344000000000\) \([2]\) \(1146880\) \(1.7620\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 187200.pt have rank \(0\).

Complex multiplication

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

Modular form 187200.2.a.pt

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