Elliptic curve isogeny class with Cremona label 188760bh (LMFDB label 188760.n)

• Label: 188760bh
• Number of curves: $4$
• Conductor: $188760$
• CM: no
• Rank: $1$

Elliptic curves in class 188760bh

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
188760.n4	188760bh1	\([0, -1, 0, 10124, -280124]\)	\(253012016/219375\)	\(-99490865760000\)	\([2]\)	\(491520\)	\(1.3735\)	\(\Gamma_0(N)\)-optimal
188760.n3	188760bh2	\([0, -1, 0, -50376, -2433924]\)	\(7793764996/3080025\)	\(5587407021081600\)	\([2, 2]\)	\(983040\)	\(1.7200\)
188760.n2	188760bh3	\([0, -1, 0, -364976, 83263116]\)	\(1481943889298/34543665\)	\(125329837488261120\)	\([2]\)	\(1966080\)	\(2.0666\)
188760.n1	188760bh4	\([0, -1, 0, -703776, -226942164]\)	\(10625310339698/3855735\)	\(13989211652782080\)	\([2]\)	\(1966080\)	\(2.0666\)

Rank

The elliptic curves in class 188760bh have rank \(1\).

Complex multiplication

The elliptic curves in class 188760bh do not have complex multiplication.

Modular form 188760.2.a.bh

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.