↑

Properties

Label 195195.g
Number of curves $4$
Conductor $195195$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

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

Elliptic curves in class 195195.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
195195.g1 195195m4 \([1, 1, 1, -31786115, -68980347610]\) \(735827390583361804729/122159491489035\) \(589640532954697539315\) \([2]\) \(22364160\) \(2.9935\)  
195195.g2 195195m3 \([1, 1, 1, -13474965, 18376144470]\) \(56059153781993690329/2200526953389765\) \(10621523303364298209885\) \([2]\) \(22364160\) \(2.9935\)  
195195.g3 195195m2 \([1, 1, 1, -2181540, -854299620]\) \(237877383098883529/72479767385025\) \(349845993531945135225\) \([2, 2]\) \(11182080\) \(2.6469\)  
195195.g4 195195m1 \([1, 1, 1, 374585, -89507020]\) \(1204244503934471/1416434394375\) \(-6836858282678799375\) \([4]\) \(5591040\) \(2.3004\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 195195.g have rank \(0\).

Complex multiplication

The elliptic curves in class 195195.g do not have complex multiplication.

Modular form 195195.2.a.g

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