Elliptic curve isogeny class with Cremona label 187200cl (LMFDB label 187200.q)

• Label: 187200cl
• Number of curves: $4$
• Conductor: $187200$
• CM: no
• Rank: $2$

Elliptic curves in class 187200cl

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
187200.q4	187200cl1	\([0, 0, 0, 6900, -470000]\)	\(12167/39\)	\(-116453376000000\)	\([2]\)	\(524288\)	\(1.3822\)	\(\Gamma_0(N)\)-optimal
187200.q3	187200cl2	\([0, 0, 0, -65100, -5510000]\)	\(10218313/1521\)	\(4541681664000000\)	\([2, 2]\)	\(1048576\)	\(1.7288\)
187200.q2	187200cl3	\([0, 0, 0, -281100, 51946000]\)	\(822656953/85683\)	\(255848067072000000\)	\([2]\)	\(2097152\)	\(2.0754\)
187200.q1	187200cl4	\([0, 0, 0, -1001100, -385526000]\)	\(37159393753/1053\)	\(3144241152000000\)	\([2]\)	\(2097152\)	\(2.0754\)

Rank

The elliptic curves in class 187200cl have rank \(2\).

Complex multiplication

The elliptic curves in class 187200cl do not have complex multiplication.

Modular form 187200.2.a.cl

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.