Properties

Label 119952.fi
Number of curves $4$
Conductor $119952$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("fi1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 119952.fi

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
119952.fi1 119952x4 \([0, 0, 0, -966819, 365834882]\) \(569001644066/122451\) \(21508397634705408\) \([2]\) \(1179648\) \(2.1287\)  
119952.fi2 119952x3 \([0, 0, 0, -437619, -108180142]\) \(52767497666/1753941\) \(308078010435299328\) \([2]\) \(1179648\) \(2.1287\)  
119952.fi3 119952x2 \([0, 0, 0, -67179, 4359530]\) \(381775972/127449\) \(11193145707856896\) \([2, 2]\) \(589824\) \(1.7821\)  
119952.fi4 119952x1 \([0, 0, 0, 12201, 469910]\) \(9148592/9639\) \(-211635107921664\) \([2]\) \(294912\) \(1.4355\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 119952.fi have rank \(1\).

Complex multiplication

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

Modular form 119952.2.a.fi

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.