Elliptic curve isogeny class with Cremona label 139650iq (LMFDB label 139650.l)

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

Elliptic curves in class 139650iq

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
139650.l4	139650iq1	\([1, 1, 0, -431225, 97753125]\)	\(4824238966273/537919488\)	\(988838903808000000\)	\([2]\)	\(2949120\)	\(2.1860\)	\(\Gamma_0(N)\)-optimal
139650.l2	139650iq2	\([1, 1, 0, -6703225, 6677081125]\)	\(18120364883707393/269485056\)	\(495385114896000000\)	\([2, 2]\)	\(5898240\)	\(2.5325\)
139650.l1	139650iq3	\([1, 1, 0, -107251225, 427470461125]\)	\(74220219816682217473/16416\)	\(30176968500000\)	\([2]\)	\(11796480\)	\(2.8791\)
139650.l3	139650iq4	\([1, 1, 0, -6507225, 7086133125]\)	\(-16576888679672833/2216253521952\)	\(-4074062665689544500000\)	\([2]\)	\(11796480\)	\(2.8791\)

Rank

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

Complex multiplication

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

Modular form 139650.2.a.iq

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.