Properties

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

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Show commands: SageMath
E = EllipticCurve("cj1")
 
E.isogeny_class()
 

Elliptic curves in class 187200.cj

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
187200.cj1 187200is1 \([0, 0, 0, -5250960300, 146455678711600]\) \(-134057911417971280740025/1872\) \(-223590481920000\) \([]\) \(51609600\) \(3.7330\) \(\Gamma_0(N)\)-optimal
187200.cj2 187200is2 \([0, 0, 0, -5116363500, 154318995790000]\) \(-198417696411528597145/22989483914821632\) \(-1716155778447868900147200000000\) \([]\) \(258048000\) \(4.5378\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 187200.2.a.cj

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

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.