Elliptic curve isogeny class with Cremona label 11552h (LMFDB label 11552.h)

• Label: 11552h
• Number of curves: $4$
• Conductor: $11552$
• CM: \(\Q(\sqrt{-1}) \)
• Rank: $0$

Rank

The elliptic curves in class 11552h have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(19\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + 3 T^{2}\)	1.3.a
\(5\)	\( 1 + 2 T + 5 T^{2}\)	1.5.c
\(7\)	\( 1 + 7 T^{2}\)	1.7.a
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 + 6 T + 13 T^{2}\)	1.13.g
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 - 10 T + 29 T^{2}\)	1.29.ak
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

Each elliptic curve in class 11552h has complex multiplication by an order in the imaginary quadratic field \(\Q(\sqrt{-1}) \).

Modular form 11552.2.a.h

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 11552h

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality	CM discriminant
11552.h3	11552h1	\([0, 0, 0, -361, 0]\)	\(1728\)	\(3010936384\)	\([2, 2]\)	\(3600\)	\(0.50826\)	\(\Gamma_0(N)\)-optimal	\(-4\)
11552.h1	11552h2	\([0, 0, 0, -3971, -96026]\)	\(287496\)	\(24087491072\)	\([2]\)	\(7200\)	\(0.85483\)		\(-16\)
11552.h2	11552h3	\([0, 0, 0, -3971, 96026]\)	\(287496\)	\(24087491072\)	\([2]\)	\(7200\)	\(0.85483\)		\(-16\)
11552.h4	11552h4	\([0, 0, 0, 1444, 0]\)	\(1728\)	\(-192699928576\)	\([2]\)	\(7200\)	\(0.85483\)		\(-4\)