Elliptic curve isogeny class with LMFDB label 78078.y (Cremona label 78078bn)

• Label: 78078.y
• Number of curves: $4$
• Conductor: $78078$
• CM: no
• Rank: $1$

Elliptic curves in class 78078.y

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
78078.y1	78078bn4	\([1, 0, 1, -6801747, 6827201500]\)	\(7209828390823479793/49509306\)	\(238971963784554\)	\([2]\)	\(1769472\)	\(2.3587\)
78078.y2	78078bn3	\([1, 0, 1, -592687, 14888564]\)	\(4770223741048753/2740574865798\)	\(13228231427407578582\)	\([2]\)	\(1769472\)	\(2.3587\)
78078.y3	78078bn2	\([1, 0, 1, -425377, 106507520]\)	\(1763535241378513/4612311396\)	\(22262746157015364\)	\([2, 2]\)	\(884736\)	\(2.0121\)
78078.y4	78078bn1	\([1, 0, 1, -16397, 2953784]\)	\(-100999381393/723148272\)	\(-3490498587624048\)	\([2]\)	\(442368\)	\(1.6656\)	\(\Gamma_0(N)\)-optimal

Rank

The elliptic curves in class 78078.y have rank \(1\).

Complex multiplication

The elliptic curves in class 78078.y do not have complex multiplication.

Modular form 78078.2.a.y

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.

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.