Properties

Label 119952.f
Number of curves $2$
Conductor $119952$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("f1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 119952.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
119952.f1 119952fs2 \([0, 0, 0, -2686719, 1694515354]\) \(40685771728/14739\) \(776990864553732864\) \([]\) \(3773952\) \(2.4015\)  
119952.f2 119952fs1 \([0, 0, 0, -93639, -8100974]\) \(1722448/459\) \(24196947339043584\) \([]\) \(1257984\) \(1.8521\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 119952.2.a.f

sage: E.q_eigenform(10)
 
\(q - 3q^{5} - 6q^{11} - 5q^{13} - q^{17} + 2q^{19} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.