Elliptic curve isogeny class with Cremona label 446400ih (LMFDB label 446400.ih)

• Label: 446400ih
• Number of curves: $6$
• Conductor: $446400$
• CM: no
• Rank: $0$

Elliptic curves in class 446400ih

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
446400.ih6	446400ih1	\([0, 0, 0, 863700, 1750462000]\)	\(23862997439/457113600\)	\(-1364933895782400000000\)	\([2]\)	\(18874368\)	\(2.7359\)	\(\Gamma_0(N)\)-optimal^*
446400.ih5	446400ih2	\([0, 0, 0, -17568300, 26781118000]\)	\(200828550012481/12454560000\)	\(37189116887040000000000\)	\([2, 2]\)	\(37748736\)	\(3.0824\)	\(\Gamma_0(N)\)-optimal^*
446400.ih2	446400ih3	\([0, 0, 0, -276768300, 1772233918000]\)	\(785209010066844481/3324675600\)	\(9927428146790400000000\)	\([2, 2]\)	\(75497472\)	\(3.4290\)	\(\Gamma_0(N)\)-optimal^*
446400.ih4	446400ih4	\([0, 0, 0, -53280300, -116709698000]\)	\(5601911201812801/1271193750000\)	\(3795764198400000000000000\)	\([2]\)	\(75497472\)	\(3.4290\)
446400.ih1	446400ih5	\([0, 0, 0, -4428288300, 113423212798000]\)	\(3216206300355197383681/57660\)	\(172171837440000000\)	\([2]\)	\(150994944\)	\(3.7756\)	\(\Gamma_0(N)\)-optimal^*
446400.ih3	446400ih6	\([0, 0, 0, -272448300, 1830234238000]\)	\(-749011598724977281/51173462246460\)	\(-152803139492533616640000000\)	\([2]\)	\(150994944\)	\(3.7756\)

^*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 446400ih1.

Rank

The elliptic curves in class 446400ih have rank \(0\).

Complex multiplication

The elliptic curves in class 446400ih do not have complex multiplication.

Modular form 446400.2.a.ih

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.