Elliptic curve isogeny class with Cremona label 81225bo (LMFDB label 81225.bh)

• Label: 81225bo
• Number of curves: $2$
• Conductor: $81225$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 81225bo have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(3\)	\(1\)
\(5\)	\(1\)
\(19\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(2\)	\( 1 - 2 T + 2 T^{2}\)	1.2.ac
\(7\)	\( 1 + 4 T + 7 T^{2}\)	1.7.e
\(11\)	\( 1 - T + 11 T^{2}\)	1.11.ab
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(23\)	\( 1 + 6 T + 23 T^{2}\)	1.23.g
\(29\)	\( 1 - 9 T + 29 T^{2}\)	1.29.aj
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 81225bo do not have complex multiplication.

Modular form 81225.2.a.bo

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 81225bo

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
81225.bh2	81225bo1	\([1, -1, 0, 25383, 54249416]\)	\(27/19\)	\(-1272719722130859375\)	\([2]\)	\(921600\)	\(2.1530\)	\(\Gamma_0(N)\)-optimal
81225.bh1	81225bo2	\([1, -1, 0, -2005242, 1067531291]\)	\(13312053/361\)	\(24181674720486328125\)	\([2]\)	\(1843200\)	\(2.4996\)