Elliptic curve isogeny class with Cremona label 11840ba (LMFDB label 11840.d)

• Label: 11840ba
• Number of curves: $2$
• Conductor: $11840$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 11840ba have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(5\)	\(1 + T\)
\(37\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 - T + 3 T^{2}\)	1.3.ab
\(7\)	\( 1 - T + 7 T^{2}\)	1.7.ab
\(11\)	\( 1 - 3 T + 11 T^{2}\)	1.11.ad
\(13\)	\( 1 - 6 T + 13 T^{2}\)	1.13.ag
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 - 2 T + 23 T^{2}\)	1.23.ac
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 11840ba do not have complex multiplication.

Modular form 11840.2.a.ba

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 Cremona numbering.

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

Isogeny graph

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

Elliptic curves in class 11840ba

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
11840.d1	11840ba1	\([0, 1, 0, -241, -1521]\)	\(94875856/185\)	\(3031040\)	\([2]\)	\(3072\)	\(0.13222\)	\(\Gamma_0(N)\)-optimal
11840.d2	11840ba2	\([0, 1, 0, -161, -2465]\)	\(-7086244/34225\)	\(-2242969600\)	\([2]\)	\(6144\)	\(0.47879\)