Elliptic curve isogeny class with Cremona label 53361bg (LMFDB label 53361.bo)

• Label: 53361bg
• Number of curves: $2$
• Conductor: $53361$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 53361bg have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(3\)	\(1\)
\(7\)	\(1\)
\(11\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(2\)	\( 1 + 2 T^{2}\)	1.2.a
\(5\)	\( 1 + 5 T^{2}\)	1.5.a
\(13\)	\( 1 - 5 T + 13 T^{2}\)	1.13.af
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 + 7 T + 19 T^{2}\)	1.19.h
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 53361bg do not have complex multiplication.

Modular form 53361.2.a.bg

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 53361bg

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
53361.bo2	53361bg1	\([1, -1, 0, 734508, 199298875]\)	\(98931640625/96059601\)	\(-42551858947602186567\)	\([2]\)	\(1228800\)	\(2.4535\)	\(\Gamma_0(N)\)-optimal
53361.bo1	53361bg2	\([1, -1, 0, -3877407, 1816236274]\)	\(14553591673375/5208653241\)	\(2307295426076181372447\)	\([2]\)	\(2457600\)	\(2.8001\)