Elliptic curve isogeny class with Cremona label 52272df (LMFDB label 52272.i)

• Label: 52272df
• Number of curves: $3$
• Conductor: $52272$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 52272df have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(11\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - 4 T + 5 T^{2}\)	1.5.ae
\(7\)	\( 1 - T + 7 T^{2}\)	1.7.ab
\(13\)	\( 1 - 3 T + 13 T^{2}\)	1.13.ad
\(17\)	\( 1 - 6 T + 17 T^{2}\)	1.17.ag
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 - 6 T + 23 T^{2}\)	1.23.ag
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 52272df do not have complex multiplication.

Modular form 52272.2.a.df

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.

\(\left(\begin{array}{rrr} 1 & 3 & 3 \\ 3 & 1 & 9 \\ 3 & 9 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels, and the \( \Gamma_0(N) \)-optimal curve is highlighted in blue.

Elliptic curves in class 52272df

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
52272.i3	52272df1	\([0, 0, 0, 2541, -34606]\)	\(9261/8\)	\(-1567363792896\)	\([]\)	\(64800\)	\(1.0276\)	\(\Gamma_0(N)\)-optimal
52272.i2	52272df2	\([0, 0, 0, -26499, 2201474]\)	\(-1167051/512\)	\(-902801544708096\)	\([]\)	\(194400\)	\(1.5769\)
52272.i1	52272df3	\([0, 0, 0, -55539, -5103054]\)	\(-132651/2\)	\(-285652051255296\)	\([]\)	\(194400\)	\(1.5769\)