Elliptic curve isogeny class with Cremona label 388311j (LMFDB label 388311.j)

• Label: 388311j
• Number of curves: $4$
• Conductor: $388311$
• CM: no
• Rank: $0$

Elliptic curves in class 388311j

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
388311.j3	388311j1	\([1, 0, 1, -74840, -5142367]\)	\(9759185353/3248553\)	\(15430965382413273\)	\([2]\)	\(2365440\)	\(1.8089\)	\(\Gamma_0(N)\)-optimal
388311.j2	388311j2	\([1, 0, 1, -486685, 126812771]\)	\(2683880485273/89699841\)	\(426083595151125681\)	\([2, 2]\)	\(4730880\)	\(2.1555\)
388311.j1	388311j3	\([1, 0, 1, -7723390, 8260869191]\)	\(10726162878394153/12605901\)	\(59879343801726141\)	\([2]\)	\(9461760\)	\(2.5021\)
388311.j4	388311j4	\([1, 0, 1, 160500, 439532563]\)	\(96260823287/17624271357\)	\(-83717126117420525037\)	\([2]\)	\(9461760\)	\(2.5021\)

Rank

The elliptic curves in class 388311j have rank \(0\).

Complex multiplication

The elliptic curves in class 388311j do not have complex multiplication.

Modular form 388311.2.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 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.