Properties

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

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Show commands: SageMath
E = EllipticCurve("qm1")
 
E.isogeny_class()
 

Elliptic curves in class 187200.qm

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
187200.qm1 187200gl2 \([0, 0, 0, -6526380, -6417363760]\) \(-6434774386429585/140608\) \(-671765181235200\) \([]\) \(4976640\) \(2.3714\)  
187200.qm2 187200gl1 \([0, 0, 0, -75180, -10031920]\) \(-9836106385/3407872\) \(-16281362025676800\) \([]\) \(1658880\) \(1.8221\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 187200.2.a.qm

sage: E.q_eigenform(10)
 
\(q + 5 q^{7} + 3 q^{11} + q^{13} + 3 q^{17} - 4 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.