Elliptic curve isogeny class with Cremona label 109200ba (LMFDB label 109200.bk)

• Label: 109200ba
• Number of curves: $2$
• Conductor: $109200$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 109200ba have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 + T\)
\(5\)	\(1\)
\(7\)	\(1 + T\)
\(13\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 - 2 T + 11 T^{2}\)	1.11.ac
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 + 10 T + 29 T^{2}\)	1.29.k
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 109200ba do not have complex multiplication.

Modular form 109200.2.a.ba

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 109200ba

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
109200.bk2	109200ba1	\([0, -1, 0, -4117888, 3217697872]\)	\(60330571443221291348/417536301\)	\(53444646528000\)	\([2]\)	\(1806336\)	\(2.2334\)	\(\Gamma_0(N)\)-optimal
109200.bk1	109200ba2	\([0, -1, 0, -4120488, 3213433872]\)	\(30222460127634675514/79352099523333\)	\(20314137477973248000\)	\([2]\)	\(3612672\)	\(2.5800\)