Properties

Label 106722.hh
Number of curves $2$
Conductor $106722$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("hh1")
 
E.isogeny_class()
 

Elliptic curves in class 106722.hh

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
106722.hh1 106722fe1 \([1, -1, 1, -11276, 463719]\) \(-67645179/8\) \(-18750201624\) \([]\) \(194400\) \(0.99673\) \(\Gamma_0(N)\)-optimal
106722.hh2 106722fe2 \([1, -1, 1, 1429, 1422523]\) \(189/512\) \(-874809406969344\) \([]\) \(583200\) \(1.5460\)  

Rank

sage: E.rank()
 

The elliptic curves in class 106722.hh have rank \(0\).

Complex multiplication

The elliptic curves in class 106722.hh do not have complex multiplication.

Modular form 106722.2.a.hh

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