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Properties

Label 259350.fw
Number of curves $2$
Conductor $259350$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("fw1")
 
E.isogeny_class()
 

Elliptic curves in class 259350.fw

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
259350.fw1 259350fw1 \([1, 0, 0, -1813, 29117]\) \(42180533641/726180\) \(11346562500\) \([2]\) \(245760\) \(0.72653\) \(\Gamma_0(N)\)-optimal
259350.fw2 259350fw2 \([1, 0, 0, -63, 83367]\) \(-1771561/192178350\) \(-3002786718750\) \([2]\) \(491520\) \(1.0731\)  

Rank

sage: E.rank()
 

The elliptic curves in class 259350.fw have rank \(0\).

Complex multiplication

The elliptic curves in class 259350.fw do not have complex multiplication.

Modular form 259350.2.a.fw

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} + q^{6} - q^{7} + q^{8} + q^{9} + q^{12} + q^{13} - q^{14} + q^{16} - 2 q^{17} + q^{18} - q^{19} + O(q^{20})\) 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 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.