Properties

Label 101568.n
Number of curves $2$
Conductor $101568$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("n1")
 
E.isogeny_class()
 

Elliptic curves in class 101568.n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
101568.n1 101568l2 \([0, -1, 0, -252278689, -1542216255071]\) \(15043017316604/243\) \(28683802819658317824\) \([2]\) \(16957440\) \(3.2790\)  
101568.n2 101568l1 \([0, -1, 0, -15752209, -24142001135]\) \(-14647977776/59049\) \(-1742541021294242807808\) \([2]\) \(8478720\) \(2.9324\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 101568.n have rank \(0\).

Complex multiplication

The elliptic curves in class 101568.n do not have complex multiplication.

Modular form 101568.2.a.n

sage: E.q_eigenform(10)
 
\(q - q^{3} - 2 q^{5} + 2 q^{7} + q^{9} - 4 q^{11} + 6 q^{13} + 2 q^{15} + 6 q^{17} - 6 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.