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Properties

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

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Show commands: SageMath
E = EllipticCurve("ct1")
 
E.isogeny_class()
 

Elliptic curves in class 259182.ct

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
259182.ct1 259182ct2 \([1, -1, 0, -1241961, -532423171]\) \(8086832279405361/226576\) \(5935854588048\) \([2]\) \(2949120\) \(1.9617\)  
259182.ct2 259182ct1 \([1, -1, 0, -77721, -8282323]\) \(1981858514481/10449152\) \(273747646884096\) \([2]\) \(1474560\) \(1.6151\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 259182.2.a.ct

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 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.