Properties

Label 106470dn
Number of curves $4$
Conductor $106470$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("dn1")
 
E.isogeny_class()
 

Elliptic curves in class 106470dn

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
106470.ff2 106470dn1 \([1, -1, 1, -17777, 915581]\) \(4767078987/6860\) \(894021562980\) \([2]\) \(221184\) \(1.1957\) \(\Gamma_0(N)\)-optimal
106470.ff3 106470dn2 \([1, -1, 1, -12707, 1444889]\) \(-1740992427/5882450\) \(-766623490255350\) \([2]\) \(442368\) \(1.5423\)  
106470.ff1 106470dn3 \([1, -1, 1, -71012, -6364601]\) \(416832723/56000\) \(5320340566632000\) \([2]\) \(663552\) \(1.7450\)  
106470.ff4 106470dn4 \([1, -1, 1, 111508, -33815609]\) \(1613964717/6125000\) \(-581912249475375000\) \([2]\) \(1327104\) \(2.0916\)  

Rank

sage: E.rank()
 

The elliptic curves in class 106470dn have rank \(1\).

Complex multiplication

The elliptic curves in class 106470dn do not have complex multiplication.

Modular form 106470.2.a.dn

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

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.