Elliptic curve isogeny class with LMFDB label 139650.cn (Cremona label 139650ga)

• Label: 139650.cn
• Number of curves: $4$
• Conductor: $139650$
• CM: no
• Rank: $1$

Elliptic curves in class 139650.cn

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
139650.cn1	139650ga4	\([1, 0, 1, -181754501, -942299826352]\)	\(361219316414914078129/378697617819360\)	\(696146813106716947500000\)	\([2]\)	\(35389440\)	\(3.4922\)
139650.cn2	139650ga2	\([1, 0, 1, -14174501, -6868266352]\)	\(171332100266282929/88068464870400\)	\(161893231617776400000000\)	\([2, 2]\)	\(17694720\)	\(3.1456\)
139650.cn3	139650ga1	\([1, 0, 1, -7902501, 8473045648]\)	\(29689921233686449/307510640640\)	\(565286240010240000000\)	\([2]\)	\(8847360\)	\(2.7990\)	\(\Gamma_0(N)\)-optimal
139650.cn4	139650ga3	\([1, 0, 1, 53053499, -53255586352]\)	\(8983747840943130191/5865547515660000\)	\(-10782434369841927187500000\)	\([2]\)	\(35389440\)	\(3.4922\)

Rank

The elliptic curves in class 139650.cn have rank \(1\).

Complex multiplication

The elliptic curves in class 139650.cn do not have complex multiplication.

Modular form 139650.2.a.cn

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.