Elliptic curve isogeny class with Cremona label 159936ka (LMFDB label 159936.eb)

• Label: 159936ka
• Number of curves: $2$
• Conductor: $159936$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 159936ka 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 \(\mathbb{F}_p\)
\(5\)	\( 1 - 3 T + 5 T^{2}\)	1.5.ad
\(11\)	\( 1 + 3 T + 11 T^{2}\)	1.11.d
\(13\)	\( 1 + 5 T + 13 T^{2}\)	1.13.f
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 - 2 T + 23 T^{2}\)	1.23.ac
\(29\)	\( 1 - 4 T + 29 T^{2}\)	1.29.ae
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 159936.2.a.ka

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 159936ka

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
159936.eb1	159936ka1	\([0, -1, 0, -66117, 6559365]\)	\(265327034368/297381\)	\(35826255123456\)	\([2]\)	\(552960\)	\(1.5149\)	\(\Gamma_0(N)\)-optimal
159936.eb2	159936ka2	\([0, -1, 0, -49457, 9928017]\)	\(-6940769488/18000297\)	\(-34696674373681152\)	\([2]\)	\(1105920\)	\(1.8614\)