Elliptic curve isogeny class with Cremona label 8880s (LMFDB label 8880.n)

• Label: 8880s
• Number of curves: $4$
• Conductor: $8880$
• CM: no
• Rank: $0$

Elliptic curves in class 8880s

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

Rank

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

Complex multiplication

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

Modular form 8880.2.a.s

Isogeny 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.

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

Isogeny graph

The vertices are labelled with Cremona labels.