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Properties

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

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Show commands: SageMath
E = EllipticCurve("t1")
 
E.isogeny_class()
 

Elliptic curves in class 105966.t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
105966.t1 105966b2 \([1, -1, 0, -1681737, -838821061]\) \(44928178875/11774\) \(137848902048359082\) \([2]\) \(1612800\) \(2.2735\)  
105966.t2 105966b1 \([1, -1, 0, -92247, -16418935]\) \(-7414875/5684\) \(-66547745816449212\) \([2]\) \(806400\) \(1.9270\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 105966.2.a.t

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