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Properties

Label 105966bc
Number of curves $2$
Conductor $105966$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("bc1")
 
E.isogeny_class()
 

Elliptic curves in class 105966bc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
105966.x2 105966bc1 \([1, -1, 0, -46008324, -205144215084]\) \(-1018411856981/1129900996\) \(-11949504603006544022766996\) \([]\) \(21436800\) \(3.5065\) \(\Gamma_0(N)\)-optimal
105966.x1 105966bc2 \([1, -1, 0, -34087320909, -2422344399910299]\) \(-414183515883649725221/50176\) \(-530646795677712946176\) \([]\) \(107184000\) \(4.3112\)  

Rank

sage: E.rank()
 

The elliptic curves in class 105966bc have rank \(0\).

Complex multiplication

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

Modular form 105966.2.a.bc

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

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.