Elliptic curve isogeny class with Cremona label 52272ch (LMFDB label 52272.m)

• Label: 52272ch
• Number of curves: $2$
• Conductor: $52272$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 52272ch have rank \(1\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - 2 T + 5 T^{2}\)	1.5.ac
\(7\)	\( 1 + 5 T + 7 T^{2}\)	1.7.f
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 - 7 T + 17 T^{2}\)	1.17.ah
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 + T + 23 T^{2}\)	1.23.b
\(29\)	\( 1 - 3 T + 29 T^{2}\)	1.29.ad
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 52272.2.a.ch

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.

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

Isogeny graph

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

Elliptic curves in class 52272ch

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
52272.m2	52272ch1	\([0, 0, 0, -11979, 380666]\)	\(8019/2\)	\(47412754735104\)	\([]\)	\(190080\)	\(1.3343\)	\(\Gamma_0(N)\)-optimal
52272.m1	52272ch2	\([0, 0, 0, -331419, -73409974]\)	\(18868971/8\)	\(1706859170463744\)	\([]\)	\(570240\)	\(1.8836\)