Elliptic curve isogeny class with LMFDB label 8993.a (Cremona label 8993a)

• Label: 8993.a
• Number of curves: $4$
• Conductor: $8993$
• CM: no
• Rank: $0$

Elliptic curves in class 8993.a

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
8993.a1	8993a3	\([1, -1, 1, -47974, 4056380]\)	\(82483294977/17\)	\(2516610113\)	\([2]\)	\(12320\)	\(1.1911\)
8993.a2	8993a2	\([1, -1, 1, -3009, 63488]\)	\(20346417/289\)	\(42782371921\)	\([2, 2]\)	\(6160\)	\(0.84454\)
8993.a3	8993a1	\([1, -1, 1, -364, -1050]\)	\(35937/17\)	\(2516610113\)	\([2]\)	\(3080\)	\(0.49796\)	\(\Gamma_0(N)\)-optimal
8993.a4	8993a4	\([1, -1, 1, -364, 169288]\)	\(-35937/83521\)	\(-12364105485169\)	\([2]\)	\(12320\)	\(1.1911\)

Rank

The elliptic curves in class 8993.a have rank \(0\).

Complex multiplication

The elliptic curves in class 8993.a do not have complex multiplication.

Modular form 8993.2.a.a

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.