Elliptic curve isogeny class with LMFDB label 8880.u (Cremona label 8880g)

• Label: 8880.u
• Number of curves: $4$
• Conductor: $8880$
• CM: no
• Rank: $1$

Elliptic curves in class 8880.u

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
8880.u1	8880g4	\([0, 1, 0, -7896, 267444]\)	\(26587051663538/14985\)	\(30689280\)	\([2]\)	\(5120\)	\(0.76313\)
8880.u2	8880g3	\([0, 1, 0, -1096, -8236]\)	\(71157653138/28112415\)	\(57574225920\)	\([2]\)	\(5120\)	\(0.76313\)
8880.u3	8880g2	\([0, 1, 0, -496, 4004]\)	\(13205172676/308025\)	\(315417600\)	\([2, 2]\)	\(2560\)	\(0.41655\)
8880.u4	8880g1	\([0, 1, 0, 4, 204]\)	\(21296/69375\)	\(-17760000\)	\([2]\)	\(1280\)	\(0.069978\)	\(\Gamma_0(N)\)-optimal

Rank

The elliptic curves in class 8880.u have rank \(1\).

Complex multiplication

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

Modular form 8880.2.a.u

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 LMFDB numbering.

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

Isogeny graph

The vertices are labelled with LMFDB labels.