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

• Label: 436800pu
• Number of curves: $4$
• Conductor: $436800$
• CM: no
• Rank: $1$

Elliptic curves in class 436800pu

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
436800.pu4	436800pu1	\([0, 1, 0, -639133, 80951363]\)	\(1804588288006144/866455078125\)	\(13863281250000000000\)	\([2]\)	\(8257536\)	\(2.3667\)	\(\Gamma_0(N)\)-optimal^*
436800.pu2	436800pu2	\([0, 1, 0, -8451633, 9448138863]\)	\(260798860029250384/196803140625\)	\(50381604000000000000\)	\([2, 2]\)	\(16515072\)	\(2.7133\)	\(\Gamma_0(N)\)-optimal^*
436800.pu1	436800pu3	\([0, 1, 0, -135201633, 605046388863]\)	\(266912903848829942596/152163375\)	\(155815296000000000\)	\([2]\)	\(33030144\)	\(3.0599\)	\(\Gamma_0(N)\)-optimal^*
436800.pu3	436800pu4	\([0, 1, 0, -6701633, 13474888863]\)	\(-32506165579682596/57814914850875\)	\(-59202472807296000000000\)	\([2]\)	\(33030144\)	\(3.0599\)

^*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 3 curves highlighted, and conditionally curve 436800pu1.

Rank

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

Complex multiplication

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

Modular form 436800.2.a.pu

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.