Elliptic curve isogeny class with LMFDB label 11200.bm (Cremona label 11200cu)

• Label: 11200.bm
• Number of curves: $2$
• Conductor: $11200$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 11200.bm have rank \(1\).

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
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 + 4 T + 13 T^{2}\)	1.13.e
\(17\)	\( 1 - 4 T + 17 T^{2}\)	1.17.ae
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 + 8 T + 23 T^{2}\)	1.23.i
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 11200.2.a.bm

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 LMFDB numbering.

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

Isogeny graph

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

Elliptic curves in class 11200.bm

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
11200.bm1	11200cu1	\([0, 0, 0, -320, 2200]\)	\(28311552/49\)	\(6272000\)	\([2]\)	\(2304\)	\(0.19825\)	\(\Gamma_0(N)\)-optimal
11200.bm2	11200cu2	\([0, 0, 0, -220, 3600]\)	\(-574992/2401\)	\(-4917248000\)	\([2]\)	\(4608\)	\(0.54482\)