Elliptic curve isogeny class with Cremona label 4400t (LMFDB label 4400.e)

• Label: 4400t
• Number of curves: $4$
• Conductor: $4400$
• CM: no
• Rank: $1$

Elliptic curves in class 4400t

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
4400.e4	4400t1	\([0, 1, 0, -1133, -14762]\)	\(643956736/15125\)	\(3781250000\)	\([2]\)	\(3456\)	\(0.62329\)	\(\Gamma_0(N)\)-optimal
4400.e3	4400t2	\([0, 1, 0, -2508, 26488]\)	\(436334416/171875\)	\(687500000000\)	\([2]\)	\(6912\)	\(0.96986\)
4400.e2	4400t3	\([0, 1, 0, -11133, 442738]\)	\(610462990336/8857805\)	\(2214451250000\)	\([2]\)	\(10368\)	\(1.1726\)
4400.e1	4400t4	\([0, 1, 0, -177508, 28726488]\)	\(154639330142416/33275\)	\(133100000000\)	\([2]\)	\(20736\)	\(1.5192\)

Rank

The elliptic curves in class 4400t have rank \(1\).

Complex multiplication

The elliptic curves in class 4400t do not have complex multiplication.

Modular form 4400.2.a.t

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.