Elliptic curve isogeny class with LMFDB label 53361.bm (Cremona label 53361bj)

• Label: 53361.bm
• Number of curves: $4$
• Conductor: $53361$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 53361.bm 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 \(\mathbb{F}_p\)
\(2\)	\( 1 - T + 2 T^{2}\)	1.2.ab
\(5\)	\( 1 + 2 T + 5 T^{2}\)	1.5.c
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 + 8 T + 23 T^{2}\)	1.23.i
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 53361.2.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 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 53361.bm

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
53361.bm1	53361bj4	\([1, -1, 0, -7818498, -8404372971]\)	\(347873904937/395307\)	\(60062912012459053467\)	\([2]\)	\(1658880\)	\(2.7086\)
53361.bm2	53361bj2	\([1, -1, 0, -614763, -58125600]\)	\(169112377/88209\)	\(13402467969722268129\)	\([2, 2]\)	\(829440\)	\(2.3620\)
53361.bm3	53361bj1	\([1, -1, 0, -347958, 78425199]\)	\(30664297/297\)	\(45126154780209657\)	\([2]\)	\(414720\)	\(2.0154\)	\(\Gamma_0(N)\)-optimal
53361.bm4	53361bj3	\([1, -1, 0, 2320092, -454331025]\)	\(9090072503/5845851\)	\(-888218104538866678731\)	\([2]\)	\(1658880\)	\(2.7086\)