Elliptic curve isogeny class with Cremona label 58800o (LMFDB label 58800.ct)

• Label: 58800o
• Number of curves: $4$
• Conductor: $58800$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 58800o have rank \(0\).

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
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 58800.2.a.o

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 58800o

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
58800.ct3	58800o1	\([0, -1, 0, -44508, -3583488]\)	\(20720464/105\)	\(49412580000000\)	\([2]\)	\(147456\)	\(1.4742\)	\(\Gamma_0(N)\)-optimal
58800.ct2	58800o2	\([0, -1, 0, -69008, 826512]\)	\(19307236/11025\)	\(20753283600000000\)	\([2, 2]\)	\(294912\)	\(1.8207\)
58800.ct4	58800o3	\([0, -1, 0, 273992, 6314512]\)	\(604223422/354375\)	\(-1334139660000000000\)	\([2]\)	\(589824\)	\(2.1673\)
58800.ct1	58800o4	\([0, -1, 0, -804008, 277186512]\)	\(15267472418/36015\)	\(135588119520000000\)	\([2]\)	\(589824\)	\(2.1673\)