Properties

Label 188760.cu
Number of curves $2$
Conductor $188760$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("cu1")
 
E.isogeny_class()
 

Elliptic curves in class 188760.cu

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
188760.cu1 188760k2 \([0, 1, 0, -24240, -1438560]\) \(434163602/7605\) \(27592133437440\) \([2]\) \(552960\) \(1.3756\)  
188760.cu2 188760k1 \([0, 1, 0, -40, -64000]\) \(-4/975\) \(-1768726502400\) \([2]\) \(276480\) \(1.0290\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 188760.cu have rank \(1\).

Complex multiplication

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

Modular form 188760.2.a.cu

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{5} + 2 q^{7} + q^{9} - q^{13} + q^{15} + 4 q^{17} - 6 q^{19} + O(q^{20})\) 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.