Properties

Label 47610.x
Number of curves $6$
Conductor $47610$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("x1")
 
E.isogeny_class()
 

Elliptic curves in class 47610.x

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
47610.x1 47610w4 \([1, -1, 0, -525614499, 4638327636393]\) \(148809678420065817601/20700\) \(2233905975776700\) \([2]\) \(6488064\) \(3.2701\)  
47610.x2 47610w6 \([1, -1, 0, -122976729, -449598702465]\) \(1905890658841300321/293666194803750\) \(31691916302207807290353750\) \([2]\) \(12976128\) \(3.6166\)  
47610.x3 47610w3 \([1, -1, 0, -33707979, 68499268785]\) \(39248884582600321/3935264062500\) \(424686468863673576562500\) \([2, 2]\) \(6488064\) \(3.2701\)  
47610.x4 47610w2 \([1, -1, 0, -32850999, 72479598093]\) \(36330796409313601/428490000\) \(46241853698577690000\) \([2, 2]\) \(3244032\) \(2.9235\)  
47610.x5 47610w1 \([1, -1, 0, -1999719, 1194630525]\) \(-8194759433281/965779200\) \(-104225117205837715200\) \([2]\) \(1622016\) \(2.5769\) \(\Gamma_0(N)\)-optimal
47610.x6 47610w5 \([1, -1, 0, 41849091, 331845880563]\) \(75108181893694559/484313964843750\) \(-52266273440413513183593750\) \([2]\) \(12976128\) \(3.6166\)  

Rank

sage: E.rank()
 

The elliptic curves in class 47610.x have rank \(0\).

Complex multiplication

The elliptic curves in class 47610.x do not have complex multiplication.

Modular form 47610.2.a.x

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} + q^{5} - q^{8} - q^{10} + 4 q^{11} - 2 q^{13} + q^{16} - 6 q^{17} - 4 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 4 & 8 \\ 8 & 1 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 2 & 4 & 2 \\ 2 & 4 & 2 & 1 & 2 & 4 \\ 4 & 8 & 4 & 2 & 1 & 8 \\ 8 & 4 & 2 & 4 & 8 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.