Elliptic curve isogeny class with Cremona label 37050bq (LMFDB label 37050.bq)

• Label: 37050bq
• Number of curves: $4$
• Conductor: $37050$
• CM: no
• Rank: $1$

Elliptic curves in class 37050bq

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
37050.bq4	37050bq1	\([1, 1, 1, 10062, 28532031]\)	\(7210309838759/22505154048000\)	\(-351643032000000000\)	\([4]\)	\(442368\)	\(2.0457\)	\(\Gamma_0(N)\)-optimal
37050.bq3	37050bq2	\([1, 1, 1, -1341938, 585556031]\)	\(17104132791725468761/400280049000000\)	\(6254375765625000000\)	\([2, 2]\)	\(884736\)	\(2.3923\)
37050.bq2	37050bq3	\([1, 1, 1, -2966938, -1110943969]\)	\(184854108796733228761/72928592456733000\)	\(1139509257136453125000\)	\([2]\)	\(1769472\)	\(2.7389\)
37050.bq1	37050bq4	\([1, 1, 1, -21348938, 37958632031]\)	\(68870385718115337310681/39076171875000\)	\(610565185546875000\)	\([2]\)	\(1769472\)	\(2.7389\)

Rank

The elliptic curves in class 37050bq have rank \(1\).

Complex multiplication

The elliptic curves in class 37050bq do not have complex multiplication.

Modular form 37050.2.a.bq

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.