Elliptic curve isogeny class with LMFDB label 258720.eb (Cremona label 258720eb)

• Label: 258720.eb
• Number of curves: $4$
• Conductor: $258720$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 258720.eb have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 - T\)
\(5\)	\(1 + T\)
\(7\)	\(1\)
\(11\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 - 6 T + 17 T^{2}\)	1.17.ag
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 - 10 T + 29 T^{2}\)	1.29.ak
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 258720.eb do not have complex multiplication.

Modular form 258720.2.a.eb

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 258720.eb

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
258720.eb1	258720eb4	\([0, 1, 0, -434900496, -3491008565220]\)	\(151020262560470148771848/35809491031875\)	\(2157030814929439680000\)	\([2]\)	\(47185920\)	\(3.4723\)
258720.eb2	258720eb2	\([0, 1, 0, -53695441, 67694931359]\)	\(35529391776305786176/16450653076171875\)	\(7927410211875000000000000\)	\([2]\)	\(47185920\)	\(3.4723\)
258720.eb3	258720eb1	\([0, 1, 0, -27281746, -54130312720]\)	\(298244193811346574784/4540317078515625\)	\(34186480894098225000000\)	\([2, 2]\)	\(23592960\)	\(3.1257\)	\(\Gamma_0(N)\)-optimal
258720.eb4	258720eb3	\([0, 1, 0, -2475496, -148850497720]\)	\(-27851742625371848/158882936571500625\)	\(-9570518325606644239680000\)	\([2]\)	\(47185920\)	\(3.4723\)