Elliptic curve isogeny class with Cremona label 435600lr (LMFDB label 435600.lr)

• Label: 435600lr
• Number of curves: $6$
• Conductor: $435600$
• CM: no
• Rank: $0$

Elliptic curves in class 435600lr

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
435600.lr6	435600lr1	\([0, 0, 0, 111068925, -42818602750]\)	\(1833318007919/1070530560\)	\(-88483579396840488960000000\)	\([2]\)	\(106168320\)	\(3.6682\)	\(\Gamma_0(N)\)-optimal^*
435600.lr5	435600lr2	\([0, 0, 0, -446499075, -343347754750]\)	\(119102750067601/68309049600\)	\(5646012771278864793600000000\)	\([2, 2]\)	\(212336640\)	\(4.0147\)	\(\Gamma_0(N)\)-optimal^*
435600.lr3	435600lr3	\([0, 0, 0, -4663107075, 122060565877250]\)	\(135670761487282321/643043610000\)	\(53150094399048197760000000000\)	\([2, 2]\)	\(424673280\)	\(4.3613\)	\(\Gamma_0(N)\)-optimal^*
435600.lr2	435600lr4	\([0, 0, 0, -5150979075, -141981127114750]\)	\(182864522286982801/463015182960\)	\(38270033789024934927360000000\)	\([2]\)	\(424673280\)	\(4.3613\)
435600.lr1	435600lr5	\([0, 0, 0, -74524635075, 7830651426925250]\)	\(553808571467029327441/12529687500\)	\(1035628164341100000000000000\)	\([2]\)	\(849346560\)	\(4.7079\)	\(\Gamma_0(N)\)-optimal^*
435600.lr4	435600lr6	\([0, 0, 0, -2267307075, 247320177277250]\)	\(-15595206456730321/310672490129100\)	\(-25678308470476884787065600000000\)	\([2]\)	\(849346560\)	\(4.7079\)

^*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 4 curves highlighted, and conditionally curve 435600lr1.

Rank

The elliptic curves in class 435600lr have rank \(0\).

Complex multiplication

The elliptic curves in class 435600lr do not have complex multiplication.

Modular form 435600.2.a.lr

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.