Properties

Label 195195.cd
Number of curves $2$
Conductor $195195$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("cd1")
 
E.isogeny_class()
 

Elliptic curves in class 195195.cd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
195195.cd1 195195ce2 \([0, 1, 1, -4527566, -70104469795]\) \(-2126464142970105856/438611057788643355\) \(-2117091801233743843704195\) \([]\) \(57600000\) \(3.3470\)  
195195.cd2 195195ce1 \([0, 1, 1, -1510916, 836633165]\) \(-79028701534867456/16987307596875\) \(-81994489194364621875\) \([]\) \(11520000\) \(2.5422\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 195195.2.a.cd

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

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.