Properties

Label 119952.y
Number of curves $3$
Conductor $119952$
CM no
Rank $0$
Graph

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

Elliptic curves in class 119952.y

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
119952.y1 119952fp3 \([0, 0, 0, -2693289459, 53800653361714]\) \(-6150311179917589675873/244053849830826\) \(-85735637053876028399394816\) \([]\) \(89579520\) \(4.0595\)  
119952.y2 119952fp2 \([0, 0, 0, -6858579, 186739099666]\) \(-101566487155393/42823570577256\) \(-15043836050558885658525696\) \([]\) \(29859840\) \(3.5102\)  
119952.y3 119952fp1 \([0, 0, 0, 761901, -6907965806]\) \(139233463487/58763045376\) \(-20643342172350490607616\) \([]\) \(9953280\) \(2.9609\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 119952.y have rank \(0\).

Complex multiplication

The elliptic curves in class 119952.y do not have complex multiplication.

Modular form 119952.2.a.y

sage: E.q_eigenform(10)
 
\(q - 3 q^{5} + 3 q^{11} - 5 q^{13} - q^{17} + 2 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.