Elliptic curve isogeny class with Cremona label 141120mi (LMFDB label 141120.fw)

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

Rank

The elliptic curves in class 141120mi 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 \(\mathbb{F}_p\)
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 + 6 T + 19 T^{2}\)	1.19.g
\(23\)	\( 1 - 6 T + 23 T^{2}\)	1.23.ag
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 141120.2.a.mi

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 141120mi

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
141120.fw1	141120mi1	\([0, 0, 0, -9408, 128968]\)	\(1048576/525\)	\(46107866649600\)	\([2]\)	\(294912\)	\(1.3146\)	\(\Gamma_0(N)\)-optimal
141120.fw2	141120mi2	\([0, 0, 0, 34692, 993328]\)	\(3286064/2205\)	\(-3098448638853120\)	\([2]\)	\(589824\)	\(1.6612\)