Properties

Label 364650ci
Number of curves $4$
Conductor $364650$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("ci1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 364650ci

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
364650.ci4 364650ci1 \([1, 0, 1, 22383399, -4475573971652]\) \(79374649975090937760383/553856914190911653543936\) \(-8654014284232994586624000000\) \([2]\) \(302579712\) \(4.0396\) \(\Gamma_0(N)\)-optimal
364650.ci3 364650ci2 \([1, 0, 1, -3942544601, -93440628435652]\) \(433744050935826360922067531137/9612122270219882316693504\) \(150189410472185661198336000000\) \([2, 2]\) \(605159424\) \(4.3861\)  
364650.ci2 364650ci3 \([1, 0, 1, -8582608601, 168305381804348]\) \(4474676144192042711273397261697/1806328356954994499451382272\) \(28223880577421789053927848000000\) \([2]\) \(1210318848\) \(4.7327\)  
364650.ci1 364650ci4 \([1, 0, 1, -62741328601, -6048934264659652]\) \(1748094148784980747354970849498497/887694600425282263291392\) \(13870228131645035363928000000\) \([2]\) \(1210318848\) \(4.7327\)  

Rank

sage: E.rank()
 

The elliptic curves in class 364650ci have rank \(0\).

Complex multiplication

The elliptic curves in class 364650ci do not have complex multiplication.

Modular form 364650.2.a.ci

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