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Properties

Label 187590.cp
Number of curves $4$
Conductor $187590$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("cp1")
 
E.isogeny_class()
 

Elliptic curves in class 187590.cp

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
187590.cp1 187590t4 \([1, 0, 0, -1772391, -405555255]\) \(127568139540190201/59114336463360\) \(285333611270374218240\) \([2]\) \(13934592\) \(2.6196\)  
187590.cp2 187590t2 \([1, 0, 0, -897816, 327346200]\) \(16581570075765001/998001000\) \(4817160208809000\) \([2]\) \(4644864\) \(2.0703\)  
187590.cp3 187590t1 \([1, 0, 0, -52816, 5739200]\) \(-3375675045001/999000000\) \(-4821982191000000\) \([2]\) \(2322432\) \(1.7237\) \(\Gamma_0(N)\)-optimal
187590.cp4 187590t3 \([1, 0, 0, 390809, -47761975]\) \(1367594037332999/995878502400\) \(-4806915318290841600\) \([2]\) \(6967296\) \(2.2730\)  

Rank

sage: E.rank()
 

The elliptic curves in class 187590.cp have rank \(1\).

Complex multiplication

The elliptic curves in class 187590.cp do not have complex multiplication.

Modular form 187590.2.a.cp

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} - q^{5} + q^{6} + 4 q^{7} + q^{8} + q^{9} - q^{10} - 6 q^{11} + q^{12} + 4 q^{14} - q^{15} + q^{16} - 6 q^{17} + q^{18} - 2 q^{19} + O(q^{20})\) 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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.