Elliptic curve isogeny class with Cremona label 193200fj (LMFDB label 193200.fy)

• Label: 193200fj
• Number of curves: $4$
• Conductor: $193200$
• CM: no
• Rank: $1$

Elliptic curves in class 193200fj

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
193200.fy3	193200fj1	\([0, 1, 0, -2348358908, 43801306114188]\)	\(358061097267989271289240144/176126855625\)	\(704507422500000000\)	\([2]\)	\(53084160\)	\(3.6619\)	\(\Gamma_0(N)\)-optimal
193200.fy2	193200fj2	\([0, 1, 0, -2348371408, 43800816489188]\)	\(89516703758060574923008036/1985322833430374025\)	\(31765165334885984400000000\)	\([2, 2]\)	\(106168320\)	\(4.0085\)
193200.fy4	193200fj3	\([0, 1, 0, -2264536408, 47072896539188]\)	\(-40133926989810174413190818/6689384645060302103835\)	\(-214060308641929667322720000000\)	\([2]\)	\(212336640\)	\(4.3550\)
193200.fy1	193200fj4	\([0, 1, 0, -2432406408, 40497400639188]\)	\(49737293673675178002921218/6641736806881023047235\)	\(212535577820192737511520000000\)	\([2]\)	\(212336640\)	\(4.3550\)

Rank

The elliptic curves in class 193200fj have rank \(1\).

Complex multiplication

The elliptic curves in class 193200fj do not have complex multiplication.

Modular form 193200.2.a.fj

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.