Properties

Label 86190.a
Number of curves $4$
Conductor $86190$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 86190.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
86190.a1 86190i4 \([1, 1, 0, -11592558, 15183418398]\) \(35694515311673154481/10400566692750\) \(50201548917665934750\) \([2]\) \(5677056\) \(2.7597\)  
86190.a2 86190i3 \([1, 1, 0, -5674178, -5081264118]\) \(4185743240664514801/113629394531250\) \(548467384187988281250\) \([2]\) \(5677056\) \(2.7597\)  
86190.a3 86190i2 \([1, 1, 0, -818808, 171275148]\) \(12577973014374481/4642947562500\) \(22410621081203062500\) \([2, 2]\) \(2838528\) \(2.4131\)  
86190.a4 86190i1 \([1, 1, 0, 158012, 19086592]\) \(90391899763439/84690294000\) \(-408783873291846000\) \([2]\) \(1419264\) \(2.0665\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 86190.a have rank \(0\).

Complex multiplication

The elliptic curves in class 86190.a do not have complex multiplication.

Modular form 86190.2.a.a

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} - q^{5} + q^{6} - 4 q^{7} - q^{8} + q^{9} + q^{10} - 4 q^{11} - q^{12} + 4 q^{14} + q^{15} + q^{16} + q^{17} - q^{18} - 4 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.