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

• Label: 262080bm
• Number of curves: $4$
• Conductor: $262080$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 262080bm have rank \(1\).

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
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 + 6 T + 23 T^{2}\)	1.23.g
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 262080.2.a.bm

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 262080bm

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
262080.bm3	262080bm1	\([0, 0, 0, -45408, 6087832]\)	\(-13870539341824/13420809675\)	\(-10018580739148800\)	\([2]\)	\(1327104\)	\(1.7664\)	\(\Gamma_0(N)\)-optimal
262080.bm2	262080bm2	\([0, 0, 0, -848028, 300488848]\)	\(5646857395652944/2031631875\)	\(24265681090560000\)	\([2]\)	\(2654208\)	\(2.1129\)
262080.bm4	262080bm3	\([0, 0, 0, 377952, -105636872]\)	\(7998456195055616/11086576921875\)	\(-8276085325872000000\)	\([2]\)	\(3981312\)	\(2.3157\)
262080.bm1	262080bm4	\([0, 0, 0, -2390268, -1043509808]\)	\(126449185587012304/33791748046875\)	\(403606476000000000000\)	\([2]\)	\(7962624\)	\(2.6622\)