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

• Label: 436800.nj
• Number of curves: $8$
• Conductor: $436800$
• CM: no
• Rank: $1$

Elliptic curves in class 436800.nj

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
436800.nj1	436800nj8	\([0, 1, 0, -3625085633, -83996196343137]\)	\(1286229821345376481036009/247265484375000000\)	\(1012799424000000000000000000\)	\([2]\)	\(382205952\)	\(4.1824\)
436800.nj2	436800nj7	\([0, 1, 0, -1594493633, 23736782344863]\)	\(109454124781830273937129/3914078300576808000\)	\(16032064719162605568000000000\)	\([2]\)	\(382205952\)	\(4.1824\)
436800.nj3	436800nj4	\([0, 1, 0, -1580549633, 24185265568863]\)	\(106607603143751752938169/5290068420\)	\(21668120248320000000\)	\([2]\)	\(127401984\)	\(3.6331\)	\(\Gamma_0(N)\)-optimal^*
436800.nj4	436800nj6	\([0, 1, 0, -250493633, -1018353655137]\)	\(424378956393532177129/136231857216000000\)	\(558005687156736000000000000\)	\([2, 2]\)	\(191102976\)	\(3.8358\)
436800.nj5	436800nj5	\([0, 1, 0, -110021633, 286567648863]\)	\(35958207000163259449/12145729518877500\)	\(49748908109322240000000000\)	\([2]\)	\(127401984\)	\(3.6331\)
436800.nj6	436800nj2	\([0, 1, 0, -98789633, 377827648863]\)	\(26031421522845051769/5797789779600\)	\(23747746937241600000000\)	\([2, 2]\)	\(63700992\)	\(3.2865\)	\(\Gamma_0(N)\)-optimal^*
436800.nj7	436800nj1	\([0, 1, 0, -5477633, 7285696863]\)	\(-4437543642183289/3033210136320\)	\(-12424028718366720000000\)	\([2]\)	\(31850496\)	\(2.9399\)	\(\Gamma_0(N)\)-optimal^*
436800.nj8	436800nj3	\([0, 1, 0, 44418367, -108550135137]\)	\(2366200373628880151/2612420149248000\)	\(-10700472931319808000000000\)	\([2]\)	\(95551488\)	\(3.4892\)

^*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 436800.nj1.

Rank

The elliptic curves in class 436800.nj have rank \(1\).

Complex multiplication

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

Modular form 436800.2.a.nj

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.