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

• Label: 446400.ew
• Number of curves: $4$
• Conductor: $446400$
• CM: no
• Rank: $1$

Elliptic curves in class 446400.ew

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
446400.ew1	446400ew4	\([0, 0, 0, -9150782700, 336926724046000]\)	\(28379906689597370652529/1357352437500\)	\(4053032660736000000000000\)	\([2]\)	\(318504960\)	\(4.1991\)	\(\Gamma_0(N)\)-optimal^*
446400.ew2	446400ew3	\([0, 0, 0, -570974700, 5282825614000]\)	\(-6894246873502147249/47925198774000\)	\(-143103876735983616000000000\)	\([2]\)	\(159252480\)	\(3.8525\)	\(\Gamma_0(N)\)-optimal^*
446400.ew3	446400ew2	\([0, 0, 0, -122846700, 376607374000]\)	\(68663623745397169/19216056254400\)	\(57378836518738329600000000\)	\([2]\)	\(106168320\)	\(3.6498\)	\(\Gamma_0(N)\)-optimal^*
446400.ew4	446400ew1	\([0, 0, 0, 20001300, 38629006000]\)	\(296354077829711/387386634240\)	\(-1156730291654492160000000\)	\([2]\)	\(53084160\)	\(3.3032\)	\(\Gamma_0(N)\)-optimal^*

^*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 4 curves highlighted, and conditionally curve 446400.ew1.

Rank

The elliptic curves in class 446400.ew have rank \(1\).

Complex multiplication

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

Modular form 446400.2.a.ew

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.