Elliptic curve isogeny class with LMFDB label 159936.gl (Cremona label 159936l)

• Label: 159936.gl
• Number of curves: $4$
• Conductor: $159936$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 159936.gl have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 - T\)
\(7\)	\(1\)
\(17\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 2 T + 5 T^{2}\)	1.5.c
\(11\)	\( 1 + 4 T + 11 T^{2}\)	1.11.e
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 159936.gl do not have complex multiplication.

Modular form 159936.2.a.gl

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.

Elliptic curves in class 159936.gl

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
159936.gl1	159936l3	\([0, 1, 0, -24818369, 41079702495]\)	\(438536015880092936/64602489661101\)	\(249050507055558542917632\)	\([2]\)	\(14155776\)	\(3.2141\)
159936.gl2	159936l2	\([0, 1, 0, -6666809, -5994553209]\)	\(68003243639904448/7163272192041\)	\(3451911414257383870464\)	\([2, 2]\)	\(7077888\)	\(2.8675\)
159936.gl3	159936l1	\([0, 1, 0, -6488204, -6363229650]\)	\(4011705594213827392/52680152007\)	\(396657101022178752\)	\([2]\)	\(3538944\)	\(2.5209\)	\(\Gamma_0(N)\)-optimal
159936.gl4	159936l4	\([0, 1, 0, 8627071, -29470659009]\)	\(18419405270942584/108003564029403\)	\(-416366962425699812868096\)	\([2]\)	\(14155776\)	\(3.2141\)