Properties

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

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Show commands: SageMath
E = EllipticCurve("mg1")
 
E.isogeny_class()
 

Elliptic curves in class 187200mg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
187200.hs1 187200mg1 \([0, 0, 0, -586200, -162295000]\) \(1909913257984/129730653\) \(1513178336592000000\) \([2]\) \(2457600\) \(2.2370\) \(\Gamma_0(N)\)-optimal
187200.hs2 187200mg2 \([0, 0, 0, 507300, -698110000]\) \(77366117936/1172914587\) \(-218894011884288000000\) \([2]\) \(4915200\) \(2.5836\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 187200.2.a.mg

sage: E.q_eigenform(10)
 
\(q - 2 q^{11} - q^{13} + 2 q^{17} - 8 q^{19} + O(q^{20})\) 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.