Elliptic curve isogeny class with Cremona label 113568s (LMFDB label 113568.m)

• Label: 113568s
• Number of curves: $4$
• Conductor: $113568$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 113568s 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 \(\mathbb{F}_p\)
\(5\)	\( 1 + 5 T^{2}\)	1.5.a
\(11\)	\( 1 + 6 T + 11 T^{2}\)	1.11.g
\(17\)	\( 1 - 8 T + 17 T^{2}\)	1.17.ai
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 - 6 T + 23 T^{2}\)	1.23.ag
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 113568.2.a.s

Isogeny matrix

The \((i,j)\)-th 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.

\(\left(\begin{array}{rrrr} 1 & 2 & 2 & 2 \\ 2 & 1 & 4 & 4 \\ 2 & 4 & 1 & 4 \\ 2 & 4 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels, and the \( \Gamma_0(N) \)-optimal curve is highlighted in blue.

Elliptic curves in class 113568s

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
113568.m3	113568s1	\([0, -1, 0, -3774, 72864]\)	\(19248832/3969\)	\(1226086714944\)	\([2, 2]\)	\(147456\)	\(1.0348\)	\(\Gamma_0(N)\)-optimal
113568.m4	113568s2	\([0, -1, 0, 8056, 427764]\)	\(23393656/45927\)	\(-113500598754816\)	\([2]\)	\(294912\)	\(1.3814\)
113568.m2	113568s3	\([0, -1, 0, -18984, -937080]\)	\(306182024/21609\)	\(53402888028672\)	\([2]\)	\(294912\)	\(1.3814\)
113568.m1	113568s4	\([0, -1, 0, -57009, 5257953]\)	\(1036433728/63\)	\(1245548408832\)	\([2]\)	\(294912\)	\(1.3814\)