Properties

Label 206910.cy
Number of curves $4$
Conductor $206910$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("cy1")
 
E.isogeny_class()
 

Elliptic curves in class 206910.cy

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
206910.cy1 206910be3 \([1, -1, 1, -3310583, 2319315221]\) \(3107086841064961/570\) \(736136742330\) \([2]\) \(3932160\) \(2.1128\)  
206910.cy2 206910be4 \([1, -1, 1, -239603, 24077837]\) \(1177918188481/488703750\) \(631145239455183750\) \([2]\) \(3932160\) \(2.1128\)  
206910.cy3 206910be2 \([1, -1, 1, -206933, 36270281]\) \(758800078561/324900\) \(419597943128100\) \([2, 2]\) \(1966080\) \(1.7662\)  
206910.cy4 206910be1 \([1, -1, 1, -10913, 751457]\) \(-111284641/123120\) \(-159005536343280\) \([2]\) \(983040\) \(1.4196\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 206910.cy have rank \(1\).

Complex multiplication

The elliptic curves in class 206910.cy do not have complex multiplication.

Modular form 206910.2.a.cy

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

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.