Properties

Label 337590.fe
Number of curves $2$
Conductor $337590$
CM no
Rank $1$
Graph

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

Elliptic curves in class 337590.fe

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
337590.fe1 337590fe2 \([1, -1, 1, -719852, -234898221]\) \(31942518433489/27900\) \(36031956335100\) \([2]\) \(3686400\) \(1.9017\)  
337590.fe2 337590fe1 \([1, -1, 1, -44672, -3716589]\) \(-7633736209/230640\) \(-297864172370160\) \([2]\) \(1843200\) \(1.5551\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 337590.fe have rank \(1\).

Complex multiplication

The elliptic curves in class 337590.fe do not have complex multiplication.

Modular form 337590.2.a.fe

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} + q^{5} + 2 q^{7} + q^{8} + q^{10} - 4 q^{13} + 2 q^{14} + q^{16} + 6 q^{17} + O(q^{20})\) 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.