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

• Label: 446400bb
• Number of curves: $4$
• Conductor: $446400$
• CM: no
• Rank: $2$

Elliptic curves in class 446400bb

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
446400.bb3	446400bb1	\([0, 0, 0, -3506700, -2527274000]\)	\(1597099875769/186000\)	\(555393024000000000\)	\([2]\)	\(10616832\)	\(2.4312\)	\(\Gamma_0(N)\)-optimal^*
446400.bb2	446400bb2	\([0, 0, 0, -3794700, -2087786000]\)	\(2023804595449/540562500\)	\(1614110976000000000000\)	\([2, 2]\)	\(21233664\)	\(2.7778\)	\(\Gamma_0(N)\)-optimal^*
446400.bb1	446400bb3	\([0, 0, 0, -21794700, 37476214000]\)	\(383432500775449/18701300250\)	\(55841783325696000000000\)	\([2]\)	\(42467328\)	\(3.1243\)	\(\Gamma_0(N)\)-optimal^*
446400.bb4	446400bb4	\([0, 0, 0, 9597300, -13524554000]\)	\(32740359775271/45410156250\)	\(-135594000000000000000000\)	\([2]\)	\(42467328\)	\(3.1243\)

^*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 446400bb1.

Rank

The elliptic curves in class 446400bb have rank \(2\).

Complex multiplication

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

Modular form 446400.2.a.bb

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.