Elliptic curve isogeny class with Cremona label 1170g (LMFDB label 1170.g)

• Label: 1170g
• Number of curves: $4$
• Conductor: $1170$
• CM: no
• Rank: $0$

Elliptic curves in class 1170g

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
1170.g3	1170g1	\([1, -1, 0, -54, -972]\)	\(-24137569/561600\)	\(-409406400\)	\([2]\)	\(384\)	\(0.33325\)	\(\Gamma_0(N)\)-optimal
1170.g2	1170g2	\([1, -1, 0, -1854, -30132]\)	\(967068262369/4928040\)	\(3592541160\)	\([2]\)	\(768\)	\(0.67982\)
1170.g4	1170g3	\([1, -1, 0, 486, 25920]\)	\(17394111071/411937500\)	\(-300302437500\)	\([6]\)	\(1152\)	\(0.88256\)
1170.g1	1170g4	\([1, -1, 0, -10764, 410670]\)	\(189208196468929/10860320250\)	\(7917173462250\)	\([6]\)	\(2304\)	\(1.2291\)

Rank

The elliptic curves in class 1170g have rank \(0\).

Complex multiplication

The elliptic curves in class 1170g do not have complex multiplication.

Modular form 1170.2.a.g

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.