Properties

Label 106742g
Number of curves $3$
Conductor $106742$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("g1")
 
E.isogeny_class()
 

Elliptic curves in class 106742g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
106742.k2 106742g1 \([1, 1, 1, -43598, 3486819]\) \(-413493625/152\) \(-3368982891608\) \([]\) \(302328\) \(1.3717\) \(\Gamma_0(N)\)-optimal
106742.k3 106742g2 \([1, 1, 1, 26627, 13329555]\) \(94196375/3511808\) \(-77836980727711232\) \([]\) \(906984\) \(1.9210\)  
106742.k1 106742g3 \([1, 1, 1, -240228, -364643867]\) \(-69173457625/2550136832\) \(-56522153672812003328\) \([]\) \(2720952\) \(2.4703\)  

Rank

sage: E.rank()
 

The elliptic curves in class 106742g have rank \(0\).

Complex multiplication

The elliptic curves in class 106742g do not have complex multiplication.

Modular form 106742.2.a.g

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} - q^{6} - q^{7} + q^{8} - 2 q^{9} - 6 q^{11} - q^{12} + 5 q^{13} - q^{14} + q^{16} + 3 q^{17} - 2 q^{18} - q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.