Properties

Label 8880.n
Number of curves $4$
Conductor $8880$
CM no
Rank $0$
Graph

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

Elliptic curves in class 8880.n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8880.n1 8880s4 \([0, -1, 0, -167800, 11865712]\) \(127568139540190201/59114336463360\) \(242132322153922560\) \([2]\) \(145152\) \(2.0303\)  
8880.n2 8880s2 \([0, -1, 0, -85000, -9509648]\) \(16581570075765001/998001000\) \(4087812096000\) \([2]\) \(48384\) \(1.4810\)  
8880.n3 8880s1 \([0, -1, 0, -5000, -165648]\) \(-3375675045001/999000000\) \(-4091904000000\) \([2]\) \(24192\) \(1.1344\) \(\Gamma_0(N)\)-optimal
8880.n4 8880s3 \([0, -1, 0, 37000, 1379952]\) \(1367594037332999/995878502400\) \(-4079118345830400\) \([2]\) \(72576\) \(1.6837\)  

Rank

sage: E.rank()
 

The elliptic curves in class 8880.n have rank \(0\).

Complex multiplication

The elliptic curves in class 8880.n do not have complex multiplication.

Modular form 8880.2.a.n

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

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.