Elliptic curve isogeny class with LMFDB label 435120.t (Cremona label 435120t)

• Label: 435120.t
• Number of curves: $4$
• Conductor: $435120$
• CM: no
• Rank: $1$

Elliptic curves in class 435120.t

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
435120.t1	435120t3	\([0, -1, 0, -261072016, 1623722749216]\)	\(8167450100737631904002/124875\)	\(30088025856000\)	\([2]\)	\(38928384\)	\(3.0658\)	\(\Gamma_0(N)\)-optimal^*
435120.t2	435120t4	\([0, -1, 0, -16562016, 24573645216]\)	\(2085187657182084002/124500749500125\)	\(29997852012421542144000\)	\([2]\)	\(38928384\)	\(3.0658\)
435120.t3	435120t2	\([0, -1, 0, -16317016, 25374697216]\)	\(3988023972023988004/15593765625\)	\(1878621114384000000\)	\([2, 2]\)	\(19464192\)	\(2.7192\)	\(\Gamma_0(N)\)-optimal^*
435120.t4	435120t1	\([0, -1, 0, -1004516, 409197216]\)	\(-3721915550952016/243896484375\)	\(-7345709437500000000\)	\([2]\)	\(9732096\)	\(2.3726\)	\(\Gamma_0(N)\)-optimal^*

^*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 3 curves highlighted, and conditionally curve 435120.t1.

Rank

The elliptic curves in class 435120.t have rank \(1\).

Complex multiplication

The elliptic curves in class 435120.t do not have complex multiplication.

Modular form 435120.2.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 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.