Properties

Label 259182.eu
Number of curves $2$
Conductor $259182$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("eu1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 259182.eu

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
259182.eu1 259182eu2 \([1, -1, 1, -30515, 253905]\) \(2433138625/1387778\) \(1792270835082882\) \([2]\) \(1075200\) \(1.6166\)  
259182.eu2 259182eu1 \([1, -1, 1, -19625, -1048539]\) \(647214625/3332\) \(4303171272708\) \([2]\) \(537600\) \(1.2701\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 259182.eu have rank \(1\).

Complex multiplication

The elliptic curves in class 259182.eu do not have complex multiplication.

Modular form 259182.2.a.eu

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.