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Properties

Label 87150.ca
Number of curves $2$
Conductor $87150$
CM no
Rank $1$
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Show commands: SageMath
E = EllipticCurve("ca1")
 
E.isogeny_class()
 

Elliptic curves in class 87150.ca

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
87150.ca1 87150bz2 \([1, 1, 1, -75838, 7545281]\) \(3087199234101529/199326394890\) \(3114474920156250\) \([2]\) \(737280\) \(1.7231\)  
87150.ca2 87150bz1 \([1, 1, 1, -14588, -539719]\) \(21973174804729/4842576900\) \(75665264062500\) \([2]\) \(368640\) \(1.3766\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 87150.ca have rank \(1\).

Complex multiplication

The elliptic curves in class 87150.ca do not have complex multiplication.

Modular form 87150.2.a.ca

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} - q^{6} - q^{7} + q^{8} + q^{9} + 2 q^{11} - q^{12} - 6 q^{13} - q^{14} + q^{16} + 4 q^{17} + q^{18} - 2 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.