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Properties

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

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

Elliptic curves in class 195195.cd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
195195.cd1 195195ce2 [0, 1, 1, -4527566, -70104469795] [] 57600000  
195195.cd2 195195ce1 [0, 1, 1, -1510916, 836633165] [] 11520000 \(\Gamma_0(N)\)-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)
 
\( q + 2q^{2} + q^{3} + 2q^{4} - q^{5} + 2q^{6} - q^{7} + q^{9} - 2q^{10} - q^{11} + 2q^{12} - 2q^{14} - q^{15} - 4q^{16} - 7q^{17} + 2q^{18} + 5q^{19} + O(q^{20}) \)

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.