Elliptic curve isogeny class with Cremona label 478800pe (LMFDB label 478800.pe)

• Label: 478800pe
• Number of curves: $4$
• Conductor: $478800$
• CM: no
• Rank: $1$

Elliptic curves in class 478800pe

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
478800.pe2	478800pe1	\([0, 0, 0, -55876875, -160766759750]\)	\(11165451838341046875/572244736\)	\(988838903808000000\)	\([2]\)	\(31850496\)	\(2.9259\)	\(\Gamma_0(N)\)-optimal^*
478800.pe3	478800pe2	\([0, 0, 0, -55780875, -161346695750]\)	\(-11108001800138902875/79947274872976\)	\(-138148890980502528000000\)	\([2]\)	\(63700992\)	\(3.2725\)
478800.pe1	478800pe3	\([0, 0, 0, -60874875, -130299441750]\)	\(19804628171203875/5638671302656\)	\(7103101904011395072000000\)	\([2]\)	\(95551488\)	\(3.4752\)	\(\Gamma_0(N)\)-optimal^*
478800.pe4	478800pe4	\([0, 0, 0, 160309125, -859543089750]\)	\(361682234074684125/462672528510976\)	\(-582834136235618598912000000\)	\([2]\)	\(191102976\)	\(3.8218\)

^*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 2 curves highlighted, and conditionally curve 478800pe1.

Rank

The elliptic curves in class 478800pe have rank \(1\).

Complex multiplication

The elliptic curves in class 478800pe do not have complex multiplication.

Modular form 478800.2.a.pe

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.