Elliptic curve isogeny class with Cremona label 187200ee (LMFDB label 187200.hi)

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

Elliptic curves in class 187200ee

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
187200.hi4	187200ee1	\([0, 0, 0, 75300, 5614000]\)	\(253012016/219375\)	\(-40940640000000000\)	\([2]\)	\(1179648\)	\(1.8751\)	\(\Gamma_0(N)\)-optimal
187200.hi3	187200ee2	\([0, 0, 0, -374700, 49714000]\)	\(7793764996/3080025\)	\(2299226342400000000\)	\([2, 2]\)	\(2359296\)	\(2.2217\)
187200.hi1	187200ee3	\([0, 0, 0, -5234700, 4608394000]\)	\(10625310339698/3855735\)	\(5756581509120000000\)	\([2]\)	\(4718592\)	\(2.5683\)
187200.hi2	187200ee4	\([0, 0, 0, -2714700, -1686566000]\)	\(1481943889298/34543665\)	\(51573415495680000000\)	\([2]\)	\(4718592\)	\(2.5683\)

Rank

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

Complex multiplication

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

Modular form 187200.2.a.ee

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.