Properties

Label 187200.bt
Number of curves $4$
Conductor $187200$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("bt1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 187200.bt

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
187200.bt1 187200kw4 \([0, 0, 0, -7488300, -7887202000]\) \(31103978031362/195\) \(291133440000000\) \([2]\) \(4718592\) \(2.3810\)  
187200.bt2 187200kw3 \([0, 0, 0, -648300, -19762000]\) \(20183398562/11567205\) \(17269744527360000000\) \([2]\) \(4718592\) \(2.3810\)  
187200.bt3 187200kw2 \([0, 0, 0, -468300, -123082000]\) \(15214885924/38025\) \(28385510400000000\) \([2, 2]\) \(2359296\) \(2.0344\)  
187200.bt4 187200kw1 \([0, 0, 0, -18300, -3382000]\) \(-3631696/24375\) \(-4548960000000000\) \([2]\) \(1179648\) \(1.6878\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 187200.bt have rank \(1\).

Complex multiplication

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

Modular form 187200.2.a.bt

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.