Properties

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

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

Elliptic curves in class 189618.p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
189618.p1 189618ba3 \([1, 0, 1, -2804481996, -57164824360694]\) \(505384091400037554067434625/815656731648\) \(3937019253229151232\) \([2]\) \(74649600\) \(3.7234\)  
189618.p2 189618ba4 \([1, 0, 1, -2804454956, -57165981802486]\) \(-505369473241574671219626625/20303219722982711328\) \(-97999763687870457882392352\) \([2]\) \(149299200\) \(4.0700\)  
189618.p3 189618ba1 \([1, 0, 1, -34720716, -77954209526]\) \(959024269496848362625/11151660319506432\) \(53826934395136521535488\) \([2]\) \(24883200\) \(3.1741\) \(\Gamma_0(N)\)-optimal
189618.p4 189618ba2 \([1, 0, 1, -7031756, -198855284470]\) \(-7966267523043306625/3534510366354604032\) \(-17060406446913699933093888\) \([2]\) \(49766400\) \(3.5207\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 189618.2.a.p

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