Elliptic curve isogeny class with LMFDB label 44400.v (Cremona label 44400c)

• Label: 44400.v
• Number of curves: $4$
• Conductor: $44400$
• CM: no
• Rank: $1$

Elliptic curves in class 44400.v

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
44400.v1	44400c4	\([0, -1, 0, -133200008, -591659581488]\)	\(8167450100737631904002/124875\)	\(3996000000000\)	\([2]\)	\(2433024\)	\(2.8975\)
44400.v2	44400c3	\([0, -1, 0, -8450008, -8950581488]\)	\(2085187657182084002/124500749500125\)	\(3984023984004000000000\)	\([2]\)	\(2433024\)	\(2.8975\)
44400.v3	44400c2	\([0, -1, 0, -8325008, -9242581488]\)	\(3988023972023988004/15593765625\)	\(249500250000000000\)	\([2, 2]\)	\(1216512\)	\(2.5510\)
44400.v4	44400c1	\([0, -1, 0, -512508, -148831488]\)	\(-3721915550952016/243896484375\)	\(-975585937500000000\)	\([2]\)	\(608256\)	\(2.2044\)	\(\Gamma_0(N)\)-optimal

Rank

The elliptic curves in class 44400.v have rank \(1\).

Complex multiplication

The elliptic curves in class 44400.v do not have complex multiplication.

Modular form 44400.2.a.v

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.