Elliptic curve isogeny class with Cremona label 178752gf (LMFDB label 178752.gt)

• Label: 178752gf
• Number of curves: $4$
• Conductor: $178752$
• CM: no
• Rank: $1$

Elliptic curves in class 178752gf

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
178752.gt3	178752gf1	\([0, 1, 0, -506529, 81016767]\)	\(466025146777/177366672\)	\(5470161887331090432\)	\([2]\)	\(2949120\)	\(2.2948\)	\(\Gamma_0(N)\)-optimal
178752.gt2	178752gf2	\([0, 1, 0, -3579809, -2550325569]\)	\(164503536215257/4178071044\)	\(128855803233712472064\)	\([2, 2]\)	\(5898240\)	\(2.6414\)
178752.gt4	178752gf3	\([0, 1, 0, 591071, -8135133889]\)	\(740480746823/927484650666\)	\(-28604535056945442717696\)	\([4]\)	\(11796480\)	\(2.9880\)
178752.gt1	178752gf4	\([0, 1, 0, -56923169, -165322254273]\)	\(661397832743623417/443352042\)	\(13673411219097649152\)	\([2]\)	\(11796480\)	\(2.9880\)

Rank

The elliptic curves in class 178752gf have rank \(1\).

Complex multiplication

The elliptic curves in class 178752gf do not have complex multiplication.

Modular form 178752.2.a.gf

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.