Properties

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

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Show commands: SageMath
E = EllipticCurve("cw1")
 
E.isogeny_class()
 

Elliptic curves in class 187200cw

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
187200.bw2 187200cw1 \([0, 0, 0, -468300, 122618000]\) \(3803721481/26000\) \(77635584000000000\) \([2]\) \(2654208\) \(2.0749\) \(\Gamma_0(N)\)-optimal
187200.bw3 187200cw2 \([0, 0, 0, -180300, 271802000]\) \(-217081801/10562500\) \(-31539456000000000000\) \([2]\) \(5308416\) \(2.4215\)  
187200.bw1 187200cw3 \([0, 0, 0, -2988300, -1908502000]\) \(988345570681/44994560\) \(134353036247040000000\) \([2]\) \(7962624\) \(2.6242\)  
187200.bw4 187200cw4 \([0, 0, 0, 1619700, -7262998000]\) \(157376536199/7722894400\) \(-23060439112089600000000\) \([2]\) \(15925248\) \(2.9708\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 187200.2.a.cw

sage: E.q_eigenform(10)
 
\(q - 4 q^{7} + 6 q^{11} + q^{13} - 6 q^{17} + 2 q^{19} + O(q^{20})\) 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 Cremona numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.