Elliptic curve isogeny class with LMFDB label 5808.bc (Cremona label 5808bf)

• Label: 5808.bc
• Number of curves: $4$
• Conductor: $5808$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 5808.bc have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 - T\)
\(11\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - 2 T + 5 T^{2}\)	1.5.ac
\(7\)	\( 1 + 4 T + 7 T^{2}\)	1.7.e
\(13\)	\( 1 - 6 T + 13 T^{2}\)	1.13.ag
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 5808.bc do not have complex multiplication.

Modular form 5808.2.a.bc

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 LMFDB numbering.

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

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 5808.bc

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
5808.bc1	5808bf3	\([0, 1, 0, -681512, -216777420]\)	\(4824238966273/66\)	\(478916714496\)	\([2]\)	\(46080\)	\(1.7971\)
5808.bc2	5808bf2	\([0, 1, 0, -42632, -3391500]\)	\(1180932193/4356\)	\(31608503156736\)	\([2, 2]\)	\(23040\)	\(1.4506\)
5808.bc3	5808bf4	\([0, 1, 0, -23272, -6465868]\)	\(-192100033/2371842\)	\(-17210829968842752\)	\([2]\)	\(46080\)	\(1.7971\)
5808.bc4	5808bf1	\([0, 1, 0, -3912, 372]\)	\(912673/528\)	\(3831333715968\)	\([2]\)	\(11520\)	\(1.1040\)	\(\Gamma_0(N)\)-optimal