Elliptic curve isogeny class with LMFDB label 432450.bu (Cremona label 432450bu)

• Label: 432450.bu
• Number of curves: $4$
• Conductor: $432450$
• CM: no
• Rank: $1$

Elliptic curves in class 432450.bu

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
432450.bu1	432450bu3	\([1, -1, 0, -1433251917, 20884865581741]\)	\(32208729120020809/658986840\)	\(6661844007844950174375000\)	\([2]\)	\(212336640\)	\(3.8827\)	\(\Gamma_0(N)\)-optimal^*
432450.bu2	432450bu2	\([1, -1, 0, -92656917, 302710546741]\)	\(8702409880009/1120910400\)	\(11331531645717062025000000\)	\([2, 2]\)	\(106168320\)	\(3.5362\)	\(\Gamma_0(N)\)-optimal^*
432450.bu3	432450bu1	\([1, -1, 0, -23464917, -38890357259]\)	\(141339344329/17141760\)	\(173289850734980160000000\)	\([2]\)	\(53084160\)	\(3.1896\)	\(\Gamma_0(N)\)-optimal^*
432450.bu4	432450bu4	\([1, -1, 0, 140866083, 1582183063741]\)	\(30579142915511/124675335000\)	\(-1260370591612742662734375000\)	\([2]\)	\(212336640\)	\(3.8827\)

^*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 432450.bu1.

Rank

The elliptic curves in class 432450.bu have rank \(1\).

Complex multiplication

The elliptic curves in class 432450.bu do not have complex multiplication.

Modular form 432450.2.a.bu

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.