Elliptic curve isogeny class with Cremona label 58800ge (LMFDB label 58800.fd)

• Label: 58800ge
• Number of curves: $4$
• Conductor: $58800$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 58800ge have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 - T\)
\(5\)	\(1\)
\(7\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 + 2 T + 11 T^{2}\)	1.11.c
\(13\)	\( 1 + 6 T + 13 T^{2}\)	1.13.g
\(17\)	\( 1 + 4 T + 17 T^{2}\)	1.17.e
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 - 2 T + 23 T^{2}\)	1.23.ac
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 58800ge do not have complex multiplication.

Modular form 58800.2.a.ge

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 58800ge

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
58800.fd4	58800ge1	\([0, -1, 0, 8167, -99588]\)	\(2048000/1323\)	\(-38912406750000\)	\([2]\)	\(165888\)	\(1.2966\)	\(\Gamma_0(N)\)-optimal
58800.fd3	58800ge2	\([0, -1, 0, -34708, -785588]\)	\(9826000/5103\)	\(2401451388000000\)	\([2]\)	\(331776\)	\(1.6432\)
58800.fd2	58800ge3	\([0, -1, 0, -138833, -20459088]\)	\(-10061824000/352947\)	\(-10380965400750000\)	\([2]\)	\(497664\)	\(1.8459\)
58800.fd1	58800ge4	\([0, -1, 0, -2239708, -1289387588]\)	\(2640279346000/3087\)	\(1452729852000000\)	\([2]\)	\(995328\)	\(2.1925\)