Elliptic curve isogeny class with LMFDB label 53550.eq (Cremona label 53550ea)

• Label: 53550.eq
• Number of curves: $4$
• Conductor: $53550$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 53550.eq have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(3\)	\(1\)
\(5\)	\(1\)
\(7\)	\(1 - T\)
\(17\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 - 4 T + 11 T^{2}\)	1.11.ae
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(19\)	\( 1 + 8 T + 19 T^{2}\)	1.19.i
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 53550.eq do not have complex multiplication.

Modular form 53550.2.a.eq

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.

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 53550.eq

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
53550.eq1	53550ea4	\([1, -1, 1, -310735730, -2108234425103]\)	\(291306206119284545407569/101150000000\)	\(1152161718750000000\)	\([2]\)	\(8257536\)	\(3.2592\)
53550.eq2	53550ea3	\([1, -1, 1, -23023730, -19866937103]\)	\(118495863754334673489/53596139570691200\)	\(610493527297404450000000\)	\([2]\)	\(8257536\)	\(3.2592\)
53550.eq3	53550ea2	\([1, -1, 1, -19423730, -32927737103]\)	\(71149857462630609489/41907496960000\)	\(477352582560000000000\)	\([2, 2]\)	\(4128768\)	\(2.9126\)
53550.eq4	53550ea1	\([1, -1, 1, -991730, -708601103]\)	\(-9470133471933009/13576123187200\)	\(-154640528179200000000\)	\([2]\)	\(2064384\)	\(2.5661\)	\(\Gamma_0(N)\)-optimal