Elliptic curve isogeny class with LMFDB label 59150.bq (Cremona label 59150be)

• Label: 59150.bq
• Number of curves: $4$
• Conductor: $59150$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 59150.bq have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(5\)	\(1\)
\(7\)	\(1 + T\)
\(13\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + 3 T^{2}\)	1.3.a
\(11\)	\( 1 + 4 T + 11 T^{2}\)	1.11.e
\(17\)	\( 1 - 6 T + 17 T^{2}\)	1.17.ag
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 + 8 T + 23 T^{2}\)	1.23.i
\(29\)	\( 1 + 10 T + 29 T^{2}\)	1.29.k
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 59150.bq do not have complex multiplication.

Modular form 59150.2.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 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.

Elliptic curves in class 59150.bq

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
59150.bq1	59150be4	\([1, -1, 1, -249839830, 1519537825797]\)	\(22868021811807457713/8953460393696\)	\(675260050147428063500000\)	\([2]\)	\(15482880\)	\(3.5372\)
59150.bq2	59150be3	\([1, -1, 1, -132215830, -573850302203]\)	\(3389174547561866673/74853681183008\)	\(5645381594019900960500000\)	\([2]\)	\(15482880\)	\(3.5372\)
59150.bq3	59150be2	\([1, -1, 1, -17971830, 16105713797]\)	\(8511781274893233/3440817243136\)	\(259502619320688016000000\)	\([2, 2]\)	\(7741440\)	\(3.1906\)
59150.bq4	59150be1	\([1, -1, 1, 3660170, 1828593797]\)	\(71903073502287/60782804992\)	\(-4584171721572352000000\)	\([2]\)	\(3870720\)	\(2.8441\)	\(\Gamma_0(N)\)-optimal