Properties

Label 188760cc
Number of curves $4$
Conductor $188760$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("cc1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 188760cc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
188760.bd4 188760cc1 \([0, -1, 0, -2460, -165900]\) \(-3631696/24375\) \(-11054540640000\) \([2]\) \(491520\) \(1.1862\) \(\Gamma_0(N)\)-optimal
188760.bd3 188760cc2 \([0, -1, 0, -62960, -6046500]\) \(15214885924/38025\) \(68980333593600\) \([2, 2]\) \(983040\) \(1.5328\)  
188760.bd2 188760cc3 \([0, -1, 0, -87160, -945140]\) \(20183398562/11567205\) \(41967634958346240\) \([2]\) \(1966080\) \(1.8793\)  
188760.bd1 188760cc4 \([0, -1, 0, -1006760, -388474260]\) \(31103978031362/195\) \(707490600960\) \([2]\) \(1966080\) \(1.8793\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 188760.2.a.cc

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

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

Isogeny graph

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

The vertices are labelled with Cremona labels.