Elliptic curve isogeny class with Cremona label 159936es (LMFDB label 159936.em)

• Label: 159936es
• Number of curves: $2$
• Conductor: $159936$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 159936es have rank \(0\).

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 \(\mathbb{F}_p\)
\(5\)	\( 1 - 3 T + 5 T^{2}\)	1.5.ad
\(11\)	\( 1 + 3 T + 11 T^{2}\)	1.11.d
\(13\)	\( 1 + T + 13 T^{2}\)	1.13.b
\(19\)	\( 1 - T + 19 T^{2}\)	1.19.ab
\(23\)	\( 1 + 9 T + 23 T^{2}\)	1.23.j
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 159936.2.a.es

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 159936es

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
159936.em2	159936es1	\([0, -1, 0, -1182337, 5164412065]\)	\(-23707171994692/1480419781911\)	\(-11414399020043287855104\)	\([2]\)	\(12976128\)	\(2.9122\)	\(\Gamma_0(N)\)-optimal
159936.em1	159936es2	\([0, -1, 0, -52620577, 145992025537]\)	\(1044942448578893426/7759962920241\)	\(119662428501237223784448\)	\([2]\)	\(25952256\)	\(3.2588\)