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

• Label: 432450gi
• Number of curves: $2$
• Conductor: $432450$
• CM: no
• Rank: $0$

Elliptic curves in class 432450gi

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
432450.gi2	432450gi1	\([1, -1, 1, -14275355, -21443972853]\)	\(-31824875809/1240000\)	\(-12535434804324375000000\)	\([2]\)	\(26542080\)	\(3.0094\)	\(\Gamma_0(N)\)-optimal^*
432450.gi1	432450gi2	\([1, -1, 1, -230500355, -1346903222853]\)	\(133974081659809/192200\)	\(1942992394670278125000\)	\([2]\)	\(53084160\)	\(3.3560\)	\(\Gamma_0(N)\)-optimal^*

^*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 2 curves highlighted, and conditionally curve 432450gi1.

Rank

The elliptic curves in class 432450gi have rank \(0\).

Complex multiplication

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

Modular form 432450.2.a.gi

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.