Elliptic curve isogeny class with Cremona label 11550cl (LMFDB label 11550.cs)

• Label: 11550cl
• Number of curves: $4$
• Conductor: $11550$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 11550cl have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(3\)	\(1 - T\)
\(5\)	\(1\)
\(7\)	\(1 + T\)
\(11\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(13\)	\( 1 - 6 T + 13 T^{2}\)	1.13.ag
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 11550cl do not have complex multiplication.

Modular form 11550.2.a.cl

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 11550cl

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
11550.cs4	11550cl1	\([1, 0, 0, -16113, -261783]\)	\(29609739866953/15259926528\)	\(238436352000000\)	\([2]\)	\(61440\)	\(1.4509\)	\(\Gamma_0(N)\)-optimal
11550.cs2	11550cl2	\([1, 0, 0, -144113, 20858217]\)	\(21184262604460873/216872764416\)	\(3388636944000000\)	\([2, 2]\)	\(122880\)	\(1.7975\)
11550.cs1	11550cl3	\([1, 0, 0, -2300113, 1342486217]\)	\(86129359107301290313/9166294368\)	\(143223349500000\)	\([2]\)	\(245760\)	\(2.1440\)
11550.cs3	11550cl4	\([1, 0, 0, -36113, 51422217]\)	\(-333345918055753/72923718045024\)	\(-1139433094453500000\)	\([2]\)	\(245760\)	\(2.1440\)