Properties

Label 100800nt
Number of curves $4$
Conductor $100800$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("nt1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 100800nt

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
100800.pl3 100800nt1 \([0, 0, 0, -8175, 142000]\) \(82881856/36015\) \(26254935000000\) \([2]\) \(294912\) \(1.2710\) \(\Gamma_0(N)\)-optimal
100800.pl2 100800nt2 \([0, 0, 0, -63300, -6032000]\) \(601211584/11025\) \(514382400000000\) \([2, 2]\) \(589824\) \(1.6176\)  
100800.pl4 100800nt3 \([0, 0, 0, -300, -17498000]\) \(-8/354375\) \(-132269760000000000\) \([2]\) \(1179648\) \(1.9642\)  
100800.pl1 100800nt4 \([0, 0, 0, -1008300, -389702000]\) \(303735479048/105\) \(39191040000000\) \([2]\) \(1179648\) \(1.9642\)  

Rank

sage: E.rank()
 

The elliptic curves in class 100800nt have rank \(0\).

Complex multiplication

The elliptic curves in class 100800nt do not have complex multiplication.

Modular form 100800.2.a.nt

sage: E.q_eigenform(10)
 
\(q + q^{7} + 4q^{11} + 6q^{13} - 6q^{17} - 4q^{19} + O(q^{20})\)  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 Cremona numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.