Properties

Label 188760.ca
Number of curves $2$
Conductor $188760$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("ca1")
 
E.isogeny_class()
 

Elliptic curves in class 188760.ca

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
188760.ca1 188760cb2 \([0, 1, 0, -4616, 31920]\) \(3991233958/2132325\) \(5812479129600\) \([2]\) \(430080\) \(1.1405\)  
188760.ca2 188760cb1 \([0, 1, 0, 1104, 4464]\) \(109083604/68445\) \(-93286702080\) \([2]\) \(215040\) \(0.79397\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 188760.ca have rank \(0\).

Complex multiplication

The elliptic curves in class 188760.ca do not have complex multiplication.

Modular form 188760.2.a.ca

sage: E.q_eigenform(10)
 
\(q + q^{3} - q^{5} + 4 q^{7} + q^{9} - q^{13} - q^{15} + 2 q^{17} + 4 q^{19} + O(q^{20})\) 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.