Elliptic curve isogeny class with Cremona label 436800hy (LMFDB label 436800.hy)

• Label: 436800hy
• Number of curves: $8$
• Conductor: $436800$
• CM: no
• Rank: $2$

Elliptic curves in class 436800hy

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
436800.hy7	436800hy1	\([0, -1, 0, -41160033, -101080728063]\)	\(1882742462388824401/11650189824000\)	\(47719177519104000000000\)	\([2]\)	\(42467328\)	\(3.1898\)	\(\Gamma_0(N)\)-optimal^*
436800.hy6	436800hy2	\([0, -1, 0, -66248033, 36727655937]\)	\(7850236389974007121/4400862921000000\)	\(18025934524416000000000000\)	\([2, 2]\)	\(84934656\)	\(3.5363\)	\(\Gamma_0(N)\)-optimal^*
436800.hy5	436800hy3	\([0, -1, 0, -254280033, 1492786151937]\)	\(443915739051786565201/21894701746029840\)	\(89680698351738224640000000\)	\([2]\)	\(127401984\)	\(3.7391\)	\(\Gamma_0(N)\)-optimal^*
436800.hy4	436800hy4	\([0, -1, 0, -794248033, 8601647655937]\)	\(13527956825588849127121/25701087819771000\)	\(105271655709782016000000000\)	\([2]\)	\(169869312\)	\(3.8829\)	\(\Gamma_0(N)\)-optimal^*
436800.hy8	436800hy5	\([0, -1, 0, 260343967, 291142823937]\)	\(476437916651992691759/284661685546875000\)	\(-1165974264000000000000000000\)	\([2]\)	\(169869312\)	\(3.8829\)
436800.hy2	436800hy6	\([0, -1, 0, -4019048033, 98070379655937]\)	\(1752803993935029634719121/4599740941532100\)	\(18840538896515481600000000\)	\([2, 2]\)	\(254803968\)	\(4.0856\)	\(\Gamma_0(N)\)-optimal^*
436800.hy1	436800hy7	\([0, -1, 0, -64304728033, 6276448294455937]\)	\(7179471593960193209684686321/49441793310\)	\(202513585397760000000\)	\([2]\)	\(509607936\)	\(4.4322\)	\(\Gamma_0(N)\)-optimal^*
436800.hy3	436800hy8	\([0, -1, 0, -3969656033, 100598212823937]\)	\(-1688971789881664420008241/89901485966373558750\)	\(-368236486518266096640000000000\)	\([2]\)	\(509607936\)	\(4.4322\)

^*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 6 curves highlighted, and conditionally curve 436800hy1.

Rank

The elliptic curves in class 436800hy have rank \(2\).

Complex multiplication

The elliptic curves in class 436800hy do not have complex multiplication.

Modular form 436800.2.a.hy

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.

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 3 & 4 & 4 & 6 & 12 & 12 \\ 2 & 1 & 6 & 2 & 2 & 3 & 6 & 6 \\ 3 & 6 & 1 & 12 & 12 & 2 & 4 & 4 \\ 4 & 2 & 12 & 1 & 4 & 6 & 3 & 12 \\ 4 & 2 & 12 & 4 & 1 & 6 & 12 & 3 \\ 6 & 3 & 2 & 6 & 6 & 1 & 2 & 2 \\ 12 & 6 & 4 & 3 & 12 & 2 & 1 & 4 \\ 12 & 6 & 4 & 12 & 3 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.