Elliptic curve isogeny class with Cremona label 111600fs (LMFDB label 111600.ey)

• Label: 111600fs
• Number of curves: $2$
• Conductor: $111600$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 111600fs have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(5\)	\(1\)
\(31\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 - 2 T + 7 T^{2}\)	1.7.ac
\(11\)	\( 1 - 2 T + 11 T^{2}\)	1.11.ac
\(13\)	\( 1 - 4 T + 13 T^{2}\)	1.13.ae
\(17\)	\( 1 + 3 T + 17 T^{2}\)	1.17.d
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 + 6 T + 23 T^{2}\)	1.23.g
\(29\)	\( 1 - 5 T + 29 T^{2}\)	1.29.af
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 111600fs do not have complex multiplication.

Modular form 111600.2.a.fs

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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 111600fs

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
111600.ey1	111600fs1	\([0, 0, 0, -82875, 23926250]\)	\(-53969305/180792\)	\(-210875788800000000\)	\([]\)	\(829440\)	\(2.0104\)	\(\Gamma_0(N)\)-optimal
111600.ey2	111600fs2	\([0, 0, 0, 727125, -560083750]\)	\(36450495095/137276928\)	\(-160119808819200000000\)	\([]\)	\(2488320\)	\(2.5597\)