Elliptic curve isogeny class with Cremona label 11200bu (LMFDB label 11200.bq)

• Label: 11200bu
• Number of curves: $4$
• Conductor: $11200$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 11200bu have rank \(0\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + 3 T^{2}\)	1.3.a
\(11\)	\( 1 + T + 11 T^{2}\)	1.11.b
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 + 4 T + 17 T^{2}\)	1.17.e
\(19\)	\( 1 - 2 T + 19 T^{2}\)	1.19.ac
\(23\)	\( 1 + 5 T + 23 T^{2}\)	1.23.f
\(29\)	\( 1 + T + 29 T^{2}\)	1.29.b
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 11200bu do not have complex multiplication.

Modular form 11200.2.a.bu

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 11200bu

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
11200.bq4	11200bu1	\([0, 0, 0, 3700, 138000]\)	\(1367631/2800\)	\(-11468800000000\)	\([2]\)	\(18432\)	\(1.1903\)	\(\Gamma_0(N)\)-optimal
11200.bq3	11200bu2	\([0, 0, 0, -28300, 1482000]\)	\(611960049/122500\)	\(501760000000000\)	\([2, 2]\)	\(36864\)	\(1.5369\)
11200.bq2	11200bu3	\([0, 0, 0, -140300, -18902000]\)	\(74565301329/5468750\)	\(22400000000000000\)	\([2]\)	\(73728\)	\(1.8834\)
11200.bq1	11200bu4	\([0, 0, 0, -428300, 107882000]\)	\(2121328796049/120050\)	\(491724800000000\)	\([2]\)	\(73728\)	\(1.8834\)