Elliptic curve isogeny class with Cremona label 47040gt (LMFDB label 47040.gj)

• Label: 47040gt
• Number of curves: $4$
• Conductor: $47040$
• CM: no
• Rank: $1$

Elliptic curves in class 47040gt

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
47040.gj4	47040gt1	\([0, 1, 0, 180, 9918]\)	\(85184/5625\)	\(-42353640000\)	\([2]\)	\(36864\)	\(0.71870\)	\(\Gamma_0(N)\)-optimal
47040.gj3	47040gt2	\([0, 1, 0, -5945, 167943]\)	\(48228544/2025\)	\(975827865600\)	\([2, 2]\)	\(73728\)	\(1.0653\)
47040.gj2	47040gt3	\([0, 1, 0, -15745, -539617]\)	\(111980168/32805\)	\(126467291381760\)	\([2]\)	\(147456\)	\(1.4118\)
47040.gj1	47040gt4	\([0, 1, 0, -94145, 11087103]\)	\(23937672968/45\)	\(173480509440\)	\([2]\)	\(147456\)	\(1.4118\)

Rank

The elliptic curves in class 47040gt have rank \(1\).

Complex multiplication

The elliptic curves in class 47040gt do not have complex multiplication.

Modular form 47040.2.a.gt

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.