Elliptic curve isogeny class with LMFDB label 262080.bj (Cremona label 262080bj)

• Label: 262080.bj
• Number of curves: $4$
• Conductor: $262080$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 262080.bj have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(5\)	\(1 + T\)
\(7\)	\(1 + T\)
\(13\)	\(1 + T\)

Good L-factors:

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

See L-function page for more information

Complex multiplication

The elliptic curves in class 262080.bj do not have complex multiplication.

Modular form 262080.2.a.bj

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 262080.bj

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
262080.bj1	262080bj4	\([0, 0, 0, -9719148, -11662376528]\)	\(531301262949272089/4740474375\)	\(905918760714240000\)	\([2]\)	\(7864320\)	\(2.6114\)
262080.bj2	262080bj2	\([0, 0, 0, -621228, -173523152]\)	\(138742439989609/12224619225\)	\(2336161114364313600\)	\([2, 2]\)	\(3932160\)	\(2.2649\)
262080.bj3	262080bj1	\([0, 0, 0, -134508, 15908272]\)	\(1408317602329/242911305\)	\(46421073289543680\)	\([2]\)	\(1966080\)	\(1.9183\)	\(\Gamma_0(N)\)-optimal
262080.bj4	262080bj3	\([0, 0, 0, 689172, -808280912]\)	\(189425802193991/1586486902455\)	\(-303182368444172206080\)	\([2]\)	\(7864320\)	\(2.6114\)