Elliptic curve isogeny class with Cremona label 212160ec (LMFDB label 212160.bt)

• Label: 212160ec
• Number of curves: $4$
• Conductor: $212160$
• CM: no
• Rank: $1$

Elliptic curves in class 212160ec

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
212160.bt3	212160ec1	\([0, -1, 0, -37601, -2790015]\)	\(22428153804601/35802000\)	\(9385279488000\)	\([2]\)	\(1032192\)	\(1.3868\)	\(\Gamma_0(N)\)-optimal
212160.bt2	212160ec2	\([0, -1, 0, -49121, -926079]\)	\(50002789171321/27473062500\)	\(7201898496000000\)	\([2, 2]\)	\(2064384\)	\(1.7334\)
212160.bt1	212160ec3	\([0, -1, 0, -473441, 124757505]\)	\(44769506062996441/323730468750\)	\(84864000000000000\)	\([2]\)	\(4128768\)	\(2.0800\)
212160.bt4	212160ec4	\([0, -1, 0, 190879, -7502079]\)	\(2933972022568679/1789082460750\)	\(-468997232590848000\)	\([2]\)	\(4128768\)	\(2.0800\)

Rank

The elliptic curves in class 212160ec have rank \(1\).

Complex multiplication

The elliptic curves in class 212160ec do not have complex multiplication.

Modular form 212160.2.a.ec

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.