Properties

Label 120666p
Number of curves $4$
Conductor $120666$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands for: SageMath
sage: E = EllipticCurve("p1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 120666p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
120666.p4 120666p1 \([1, 1, 0, 166, 221460]\) \(103823/4386816\) \(-21174322950144\) \([2]\) \(368640\) \(1.2359\) \(\Gamma_0(N)\)-optimal
120666.p3 120666p2 \([1, 1, 0, -53914, 4710100]\) \(3590714269297/73410624\) \(354339060618816\) \([2, 2]\) \(737280\) \(1.5825\)  
120666.p2 120666p3 \([1, 1, 0, -114754, -7956788]\) \(34623662831857/14438442312\) \(69691603297542408\) \([2]\) \(1474560\) \(1.9290\)  
120666.p1 120666p4 \([1, 1, 0, -858354, 305731548]\) \(14489843500598257/6246072\) \(30148596544248\) \([2]\) \(1474560\) \(1.9290\)  

Rank

sage: E.rank()
 

The elliptic curves in class 120666p have rank \(1\).

Complex multiplication

The elliptic curves in class 120666p do not have complex multiplication.

Modular form 120666.2.a.p

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