Elliptic curve isogeny class with Cremona label 141120bb (LMFDB label 141120.lw)

• Label: 141120bb
• Number of curves: $2$
• Conductor: $141120$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 141120bb have rank \(1\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 + 4 T + 11 T^{2}\)	1.11.e
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 + 8 T + 23 T^{2}\)	1.23.i
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 141120bb do not have complex multiplication.

Modular form 141120.2.a.bb

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.

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

Isogeny graph

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

Elliptic curves in class 141120bb

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
141120.lw2	141120bb1	\([0, 0, 0, 168, 1694]\)	\(229376/675\)	\(-1543147200\)	\([]\)	\(55296\)	\(0.44649\)	\(\Gamma_0(N)\)-optimal
141120.lw1	141120bb2	\([0, 0, 0, -7392, 245126]\)	\(-19539165184/46875\)	\(-107163000000\)	\([]\)	\(165888\)	\(0.99580\)