Elliptic curve isogeny class with Cremona label 52416fx (LMFDB label 52416.fl)

• Label: 52416fx
• Number of curves: $2$
• Conductor: $52416$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 52416fx have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(7\)	\(1 + T\)
\(13\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - 3 T + 5 T^{2}\)	1.5.ad
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 - 5 T + 19 T^{2}\)	1.19.af
\(23\)	\( 1 + 3 T + 23 T^{2}\)	1.23.d
\(29\)	\( 1 - T + 29 T^{2}\)	1.29.ab
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 52416fx do not have complex multiplication.

Modular form 52416.2.a.fx

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 52416fx

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
52416.fl1	52416fx1	\([0, 0, 0, -184539, -30512680]\)	\(14896378491692608/138411\)	\(6457703616\)	\([2]\)	\(122880\)	\(1.4629\)	\(\Gamma_0(N)\)-optimal
52416.fl2	52416fx2	\([0, 0, 0, -184404, -30559552]\)	\(-232245467895232/709540923\)	\(-2118677843423232\)	\([2]\)	\(245760\)	\(1.8094\)