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Properties

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

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Show commands: SageMath
E = EllipticCurve("bb1")
 
E.isogeny_class()
 

Elliptic curves in class 105966bb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
105966.d2 105966bb1 \([1, -1, 0, -25594731, -30307156619]\) \(6045996937/2204496\) \(676109164063411369794384\) \([]\) \(22049280\) \(3.2730\) \(\Gamma_0(N)\)-optimal
105966.d1 105966bb2 \([1, -1, 0, -884941146, 10131464200756]\) \(249896037845497/37933056\) \(11633900348438178631962624\) \([]\) \(66147840\) \(3.8223\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 105966.2.a.bb

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - 3 q^{5} + q^{7} - q^{8} + 3 q^{10} + 6 q^{11} + 2 q^{13} - q^{14} + q^{16} + 3 q^{17} - 2 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.