Elliptic curve isogeny class with Cremona label 58800fq (LMFDB label 58800.br)

• Label: 58800fq
• Number of curves: $2$
• Conductor: $58800$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 58800fq 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 \(\mathbb{F}_p\)
\(11\)	\( 1 + 4 T + 11 T^{2}\)	1.11.e
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 - 8 T + 23 T^{2}\)	1.23.ai
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 58800.2.a.fq

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.

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

Isogeny graph

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

Elliptic curves in class 58800fq

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
58800.br1	58800fq1	\([0, -1, 0, -6533, 76812]\)	\(1048576/525\)	\(15441431250000\)	\([2]\)	\(110592\)	\(1.2235\)	\(\Gamma_0(N)\)-optimal
58800.br2	58800fq2	\([0, -1, 0, 24092, 566812]\)	\(3286064/2205\)	\(-1037664180000000\)	\([2]\)	\(221184\)	\(1.5700\)