Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("j1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 189618j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
189618.br3 189618j1 \([1, 0, 0, -16955013, 17399039553]\) \(111675519439697265625/37528570137307392\) \(181143240095886555472128\) \([2]\) \(25546752\) \(3.1652\) \(\Gamma_0(N)\)-optimal
189618.br4 189618j2 \([1, 0, 0, 49468747, 120262874289]\) \(2773679829880629422375/2899504554614368272\) \(-13995354679753624304604048\) \([2]\) \(51093504\) \(3.5118\)  
189618.br1 189618j3 \([1, 0, 0, -556892268, -5057497008240]\) \(3957101249824708884951625/772310238681366528\) \(3727794010859368089649152\) \([2]\) \(76640256\) \(3.7145\)  
189618.br2 189618j4 \([1, 0, 0, -498053228, -6167895603312]\) \(-2830680648734534916567625/1766676274677722124288\) \(-8527408942700901249012436992\) \([2]\) \(153280512\) \(4.0611\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 189618.2.a.j

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

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.