Properties

Label 189618.n
Number of curves $4$
Conductor $189618$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("n1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 189618.n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
189618.n1 189618x4 \([1, 0, 1, -237317747, -1407179633650]\) \(306234591284035366263793/1727485056\) \(8338240415666304\) \([2]\) \(24772608\) \(3.1247\)  
189618.n2 189618x2 \([1, 0, 1, -14832627, -21987276530]\) \(74768347616680342513/5615307472896\) \(27104016647941668864\) \([2, 2]\) \(12386304\) \(2.7782\)  
189618.n3 189618x3 \([1, 0, 1, -13859187, -24997542386]\) \(-60992553706117024753/20624795251201152\) \(-99551947341654981283968\) \([2]\) \(24772608\) \(3.1247\)  
189618.n4 189618x1 \([1, 0, 1, -988147, -295745266]\) \(22106889268753393/4969545596928\) \(23987047413162442752\) \([2]\) \(6193152\) \(2.4316\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 189618.n have rank \(0\).

Complex multiplication

The elliptic curves in class 189618.n do not have complex multiplication.

Modular form 189618.2.a.n

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - 2q^{5} - q^{6} - 4q^{7} - q^{8} + q^{9} + 2q^{10} + q^{11} + q^{12} + 4q^{14} - 2q^{15} + q^{16} + q^{17} - q^{18} + 4q^{19} + O(q^{20})\)  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 LMFDB 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 LMFDB labels.