Elliptic curve isogeny class with Cremona label 113568w (LMFDB label 113568.bn)

• Label: 113568w
• Number of curves: $2$
• Conductor: $113568$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 113568w have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 + T\)
\(7\)	\(1 - T\)
\(13\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - T + 5 T^{2}\)	1.5.ab
\(11\)	\( 1 + T + 11 T^{2}\)	1.11.b
\(17\)	\( 1 + 5 T + 17 T^{2}\)	1.17.f
\(19\)	\( 1 - 3 T + 19 T^{2}\)	1.19.ad
\(23\)	\( 1 + 7 T + 23 T^{2}\)	1.23.h
\(29\)	\( 1 + 5 T + 29 T^{2}\)	1.29.f
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 113568w do not have complex multiplication.

Modular form 113568.2.a.w

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 113568w

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
113568.bn2	113568w1	\([0, -1, 0, 35434, -3733692]\)	\(15926924096/28588707\)	\(-8831502607741632\)	\([2]\)	\(1105920\)	\(1.7446\)	\(\Gamma_0(N)\)-optimal
113568.bn1	113568w2	\([0, -1, 0, -254401, -38803727]\)	\(92100460096/20253807\)	\(400430112406990848\)	\([2]\)	\(2211840\)	\(2.0911\)