Properties

Label 187200ge
Number of curves $4$
Conductor $187200$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("ge1")
 
E.isogeny_class()
 

Elliptic curves in class 187200ge

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
187200.pp4 187200ge1 \([0, 0, 0, 2934825, -1376507000]\) \(3834800837445824/3342041015625\) \(-2436347900390625000000\) \([2]\) \(9437184\) \(2.7912\) \(\Gamma_0(N)\)-optimal
187200.pp3 187200ge2 \([0, 0, 0, -14643300, -12204632000]\) \(7442744143086784/2927948765625\) \(136606377609000000000000\) \([2, 2]\) \(18874368\) \(3.1378\)  
187200.pp2 187200ge3 \([0, 0, 0, -105768300, 410068618000]\) \(350584567631475848/8259273550125\) \(3082757334037056000000000\) \([2]\) \(37748736\) \(3.4844\)  
187200.pp1 187200ge4 \([0, 0, 0, -204768300, -1127477882000]\) \(2543984126301795848/909361981125\) \(339417540730944000000000\) \([2]\) \(37748736\) \(3.4844\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 187200.2.a.ge

sage: E.q_eigenform(10)
 
\(q + 4 q^{7} + q^{13} + 2 q^{17} + 8 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.