Elliptic curve isogeny class with LMFDB label 338130.j (Cremona label 338130j)

• Label: 338130.j
• Number of curves: $4$
• Conductor: $338130$
• CM: no
• Rank: $1$

Elliptic curves in class 338130.j

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
338130.j1	338130j4	\([1, -1, 0, -3110850, 2005178386]\)	\(189208196468929/10860320250\)	\(191101320730028270250\)	\([2]\)	\(11943936\)	\(2.6457\)
338130.j2	338130j2	\([1, -1, 0, -535860, -150181880]\)	\(967068262369/4928040\)	\(86715210134840040\)	\([2]\)	\(3981312\)	\(2.0964\)
338130.j3	338130j1	\([1, -1, 0, -15660, -4838000]\)	\(-24137569/561600\)	\(-9882075229041600\)	\([2]\)	\(1990656\)	\(1.7499\)	\(\Gamma_0(N)\)-optimal
338130.j4	338130j3	\([1, -1, 0, 140400, 127906636]\)	\(17394111071/411937500\)	\(-7248570806024437500\)	\([2]\)	\(5971968\)	\(2.2992\)

Rank

The elliptic curves in class 338130.j have rank \(1\).

Complex multiplication

The elliptic curves in class 338130.j do not have complex multiplication.

Modular form 338130.2.a.j

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 LMFDB numbering.

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

Isogeny graph

The vertices are labelled with LMFDB labels.