Elliptic curve isogeny class with LMFDB label 428400.gi (Cremona label 428400gi)

• Label: 428400.gi
• Number of curves: $6$
• Conductor: $428400$
• CM: no
• Rank: $0$

Elliptic curves in class 428400.gi

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
428400.gi1	428400gi6	\([0, 0, 0, -6273288075, -191245147159750]\)	\(585196747116290735872321/836876053125000\)	\(39045289134600000000000000\)	\([2]\)	\(339738624\)	\(4.1818\)
428400.gi2	428400gi3	\([0, 0, 0, -909432075, 10554421720250]\)	\(1782900110862842086081/328139630024640\)	\(15309682578429603840000000\)	\([4]\)	\(169869312\)	\(3.8353\)	\(\Gamma_0(N)\)-optimal^*
428400.gi3	428400gi4	\([0, 0, 0, -395640075, -2931182887750]\)	\(146796951366228945601/5397929064360000\)	\(251845778426780160000000000\)	\([2, 2]\)	\(169869312\)	\(3.8353\)
428400.gi4	428400gi2	\([0, 0, 0, -62712075, 128758360250]\)	\(584614687782041281/184812061593600\)	\(8622591545711001600000000\)	\([2, 2]\)	\(84934656\)	\(3.4887\)	\(\Gamma_0(N)\)-optimal^*
428400.gi5	428400gi1	\([0, 0, 0, 11015925, 13668952250]\)	\(3168685387909439/3563732336640\)	\(-166269495898275840000000\)	\([2]\)	\(42467328\)	\(3.1421\)	\(\Gamma_0(N)\)-optimal^*
428400.gi6	428400gi5	\([0, 0, 0, 155159925, -10453458487750]\)	\(8854313460877886399/1016927675429790600\)	\(-47445777624852310233600000000\)	\([2]\)	\(339738624\)	\(4.1818\)

^*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 0 curves highlighted, and conditionally curve 428400.gi1.

Rank

The elliptic curves in class 428400.gi have rank \(0\).

Complex multiplication

The elliptic curves in class 428400.gi do not have complex multiplication.

Modular form 428400.2.a.gi

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.

\(\left(\begin{array}{rrrrrr} 1 & 8 & 2 & 4 & 8 & 4 \\ 8 & 1 & 4 & 2 & 4 & 8 \\ 2 & 4 & 1 & 2 & 4 & 2 \\ 4 & 2 & 2 & 1 & 2 & 4 \\ 8 & 4 & 4 & 2 & 1 & 8 \\ 4 & 8 & 2 & 4 & 8 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.