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Properties

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

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Show commands: SageMath
E = EllipticCurve("bj1")
 
E.isogeny_class()
 

Elliptic curves in class 195195.bj

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
195195.bj1 195195u2 \([0, 1, 1, -142185, -20684569]\) \(-65860951343104/3493875\) \(-16864267294875\) \([]\) \(933120\) \(1.6058\)  
195195.bj2 195195u1 \([0, 1, 1, -225, -75526]\) \(-262144/509355\) \(-2458559298195\) \([]\) \(311040\) \(1.0565\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 195195.2.a.bj

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

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.