Properties

Label 297920gu
Number of curves $2$
Conductor $297920$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("gu1")
 
E.isogeny_class()
 

Elliptic curves in class 297920gu

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
297920.gu1 297920gu1 \([0, -1, 0, -180581, -27486619]\) \(5405726654464/407253125\) \(49062833052800000\) \([2]\) \(2764800\) \(1.9479\) \(\Gamma_0(N)\)-optimal
297920.gu2 297920gu2 \([0, -1, 0, 173199, -122370415]\) \(298091207216/3525390625\) \(-6795406240000000000\) \([2]\) \(5529600\) \(2.2945\)  

Rank

sage: E.rank()
 

The elliptic curves in class 297920gu have rank \(0\).

Complex multiplication

The elliptic curves in class 297920gu do not have complex multiplication.

Modular form 297920.2.a.gu

sage: E.q_eigenform(10)
 
\(q + 2 q^{3} - q^{5} + q^{9} + 6 q^{13} - 2 q^{15} - 2 q^{17} - q^{19} + O(q^{20})\) 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 Cremona 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 Cremona labels.