Elliptic curve isogeny class with Cremona label 134640by (LMFDB label 134640.n)

• Label: 134640by
• Number of curves: $4$
• Conductor: $134640$
• CM: no
• Rank: $1$

Elliptic curves in class 134640by

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
134640.n3	134640by1	\([0, 0, 0, -6321243, 10353164042]\)	\(-9354997870579612441/10093752054144000\)	\(-30139782133641117696000\)	\([2]\)	\(8847360\)	\(3.0082\)	\(\Gamma_0(N)\)-optimal
134640.n2	134640by2	\([0, 0, 0, -119516763, 502731036938]\)	\(63229930193881628103961/26218934428500000\)	\(78289318700550144000000\)	\([2]\)	\(17694720\)	\(3.3548\)
134640.n4	134640by3	\([0, 0, 0, 52981557, -186985954438]\)	\(5508208700580085578359/8246033269590589440\)	\(-24622523406465186618408960\)	\([2]\)	\(26542080\)	\(3.5575\)
134640.n1	134640by4	\([0, 0, 0, -348098763, -1878822960262]\)	\(1562225332123379392365961/393363080510106009600\)	\(1174575864593888382969446400\)	\([2]\)	\(53084160\)	\(3.9041\)

Rank

The elliptic curves in class 134640by have rank \(1\).

Complex multiplication

The elliptic curves in class 134640by do not have complex multiplication.

Modular form 134640.2.a.by

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.