Elliptic curve isogeny class with Cremona label 53361m (LMFDB label 53361.bv)

• Label: 53361m
• Number of curves: $2$
• Conductor: $53361$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 53361m have rank \(1\).

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.b
\(5\)	\( 1 + 4 T + 5 T^{2}\)	1.5.e
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 + 6 T + 19 T^{2}\)	1.19.g
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 53361.2.a.m

Isogeny matrix

The \((i,j)\)-th 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, and the \( \Gamma_0(N) \)-optimal curve is highlighted in blue.

Elliptic curves in class 53361m

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
53361.bv2	53361m1	\([1, -1, 0, -10005, -68832]\)	\(19683/11\)	\(61901446886433\)	\([2]\)	\(172800\)	\(1.3366\)	\(\Gamma_0(N)\)-optimal
53361.bv1	53361m2	\([1, -1, 0, -98940, 11937393]\)	\(19034163/121\)	\(680915915750763\)	\([2]\)	\(345600\)	\(1.6832\)