Elliptic curve isogeny class with Cremona label 115600by (LMFDB label 115600.ct)

• Label: 115600by
• Number of curves: $4$
• Conductor: $115600$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 115600by have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(5\)	\(1\)
\(17\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 - T + 3 T^{2}\)	1.3.ab
\(7\)	\( 1 + 3 T + 7 T^{2}\)	1.7.d
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 + T + 13 T^{2}\)	1.13.b
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
\(29\)	\( 1 + 4 T + 29 T^{2}\)	1.29.e
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 115600by do not have complex multiplication.

Modular form 115600.2.a.by

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 115600by

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
115600.ct2	115600by1	\([0, -1, 0, -295187008, -1951936447488]\)	\(1841373668746009/31443200\)	\(48573594213171200000000\)	\([2]\)	\(26542080\)	\(3.4826\)	\(\Gamma_0(N)\)-optimal
115600.ct3	115600by2	\([0, -1, 0, -285939008, -2079965759488]\)	\(-1673672305534489/241375690000\)	\(-372878231827047040000000000\)	\([2]\)	\(53084160\)	\(3.8292\)
115600.ct1	115600by3	\([0, -1, 0, -481881008, 801033624512]\)	\(8010684753304969/4456448000000\)	\(6884340550074368000000000000\)	\([2]\)	\(79626240\)	\(4.0320\)
115600.ct4	115600by4	\([0, -1, 0, 1885606992, 6340955544512]\)	\(479958568556831351/289000000000000\)	\(-446448476224000000000000000000\)	\([2]\)	\(159252480\)	\(4.3785\)