Elliptic curve isogeny class with Cremona label 43320t (LMFDB label 43320.e)

• Label: 43320t
• Number of curves: $4$
• Conductor: $43320$
• CM: no
• Rank: $1$

Elliptic curves in class 43320t

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
43320.e4	43320t1	\([0, -1, 0, 1324, 8196]\)	\(21296/15\)	\(-180656183040\)	\([2]\)	\(55296\)	\(0.84848\)	\(\Gamma_0(N)\)-optimal
43320.e3	43320t2	\([0, -1, 0, -5896, 74620]\)	\(470596/225\)	\(10839370982400\)	\([2, 2]\)	\(110592\)	\(1.1950\)
43320.e2	43320t3	\([0, -1, 0, -49216, -4136084]\)	\(136835858/1875\)	\(180656183040000\)	\([2]\)	\(221184\)	\(1.5416\)
43320.e1	43320t4	\([0, -1, 0, -78096, 8420940]\)	\(546718898/405\)	\(39021735536640\)	\([2]\)	\(221184\)	\(1.5416\)

Rank

The elliptic curves in class 43320t have rank \(1\).

Complex multiplication

The elliptic curves in class 43320t do not have complex multiplication.

Modular form 43320.2.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.

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

Isogeny graph

The vertices are labelled with Cremona labels.