Properties

Label 105966.p
Number of curves $2$
Conductor $105966$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("p1")
 
E.isogeny_class()
 

Elliptic curves in class 105966.p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
105966.p1 105966p2 \([1, -1, 0, -5721147, -4639750605]\) \(1164800512406592125/150691848242418\) \(2679237921865778466858\) \([2]\) \(6623232\) \(2.8402\)  
105966.p2 105966p1 \([1, -1, 0, 545463, -379709127]\) \(1009479798755875/4084868810988\) \(-72627255899334836028\) \([2]\) \(3311616\) \(2.4937\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 105966.p have rank \(1\).

Complex multiplication

The elliptic curves in class 105966.p do not have complex multiplication.

Modular form 105966.2.a.p

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - q^{7} - q^{8} - 4 q^{11} + 2 q^{13} + q^{14} + q^{16} + 6 q^{17} + 4 q^{19} + O(q^{20})\) 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.