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Properties

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

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Show commands: SageMath
E = EllipticCurve("ed1")
 
E.isogeny_class()
 

Elliptic curves in class 259182ed

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
259182.ed2 259182ed1 \([1, -1, 1, -8636, 309631]\) \(1981858514481/10449152\) \(375511175424\) \([2]\) \(491520\) \(1.0658\) \(\Gamma_0(N)\)-optimal
259182.ed1 259182ed2 \([1, -1, 1, -137996, 19765375]\) \(8086832279405361/226576\) \(8142461712\) \([2]\) \(983040\) \(1.4124\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 259182.2.a.ed

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} - 2 q^{5} + q^{7} + q^{8} - 2 q^{10} + 4 q^{13} + q^{14} + q^{16} - q^{17} - 6 q^{19} + O(q^{20})\) 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.