Elliptic curve isogeny class with LMFDB label 11200.be (Cremona label 11200cn)

• Label: 11200.be
• Number of curves: $3$
• Conductor: $11200$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 11200.be 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 \(\mathbb{F}_p\)
\(3\)	\( 1 + T + 3 T^{2}\)	1.3.b
\(11\)	\( 1 + 3 T + 11 T^{2}\)	1.11.d
\(13\)	\( 1 - 5 T + 13 T^{2}\)	1.13.af
\(17\)	\( 1 + 3 T + 17 T^{2}\)	1.17.d
\(19\)	\( 1 - 2 T + 19 T^{2}\)	1.19.ac
\(23\)	\( 1 + 6 T + 23 T^{2}\)	1.23.g
\(29\)	\( 1 + 3 T + 29 T^{2}\)	1.29.d
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 11200.2.a.be

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 LMFDB numbering.

\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 11200.be

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
11200.be1	11200cn3	\([0, -1, 0, -13133, 610387]\)	\(-250523582464/13671875\)	\(-13671875000000\)	\([]\)	\(20736\)	\(1.2788\)
11200.be2	11200cn1	\([0, -1, 0, -133, -613]\)	\(-262144/35\)	\(-35000000\)	\([]\)	\(2304\)	\(0.18014\)	\(\Gamma_0(N)\)-optimal
11200.be3	11200cn2	\([0, -1, 0, 867, 1387]\)	\(71991296/42875\)	\(-42875000000\)	\([]\)	\(6912\)	\(0.72945\)