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Properties

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

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Show commands: SageMath
E = EllipticCurve("y1")
 
E.isogeny_class()
 

Elliptic curves in class 189618.y

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
189618.y1 189618m3 \([1, 1, 1, -81785779, 284644874405]\) \(12534210458299016895673/315581882565708\) \(1523253471005102465772\) \([2]\) \(29491200\) \(3.1727\)  
189618.y2 189618m2 \([1, 1, 1, -5306519, 4088357021]\) \(3423676911662954233/483711578981136\) \(2334783402830358075024\) \([2, 2]\) \(14745600\) \(2.8262\)  
189618.y3 189618m1 \([1, 1, 1, -1399239, -573809475]\) \(62768149033310713/6915442583808\) \(33379520502507708672\) \([2]\) \(7372800\) \(2.4796\) \(\Gamma_0(N)\)-optimal
189618.y4 189618m4 \([1, 1, 1, 8656261, 21988640981]\) \(14861225463775641287/51859390496937804\) \(-250315372785133864787436\) \([2]\) \(29491200\) \(3.1727\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 189618.2.a.y

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