Elliptic curve isogeny class with Cremona label 53816a (LMFDB label 53816.a)

• Label: 53816a
• Number of curves: $2$
• Conductor: $53816$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 53816a have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(7\)	\(1 - T\)
\(31\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + 2 T + 3 T^{2}\)	1.3.c
\(5\)	\( 1 + 4 T + 5 T^{2}\)	1.5.e
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 + 13 T^{2}\)	1.13.a
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 + 2 T + 19 T^{2}\)	1.19.c
\(23\)	\( 1 + 8 T + 23 T^{2}\)	1.23.i
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 53816a do not have complex multiplication.

Modular form 53816.2.a.a

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 53816a

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
53816.a2	53816a1	\([0, 1, 0, -320, 121264]\)	\(-4/7\)	\(-6361626385408\)	\([2]\)	\(120960\)	\(1.1358\)	\(\Gamma_0(N)\)-optimal
53816.a1	53816a2	\([0, 1, 0, -38760, 2888944]\)	\(3543122/49\)	\(89062769395712\)	\([2]\)	\(241920\)	\(1.4823\)