Properties

Label 369600.fe
Number of curves $2$
Conductor $369600$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("fe1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 369600.fe

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
369600.fe1 369600fe2 \([0, -1, 0, -3547633, -2082282863]\) \(19288565375865424/3837216796875\) \(982327500000000000000\) \([2]\) \(13271040\) \(2.7443\)  
369600.fe2 369600fe1 \([0, -1, 0, 461867, -193808363]\) \(681010157060096/1406657896875\) \(-22506526350000000000\) \([2]\) \(6635520\) \(2.3977\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 369600.fe have rank \(0\).

Complex multiplication

The elliptic curves in class 369600.fe do not have complex multiplication.

Modular form 369600.2.a.fe

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{7} + q^{9} + q^{11} + 2 q^{13} - 2 q^{17} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.