Elliptic curve isogeny class with Cremona label 141120bk (LMFDB label 141120.mq)

• Label: 141120bk
• Number of curves: $4$
• Conductor: $141120$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 141120bk 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
\(13\)	\( 1 - 4 T + 13 T^{2}\)	1.13.ae
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 141120.2.a.bk

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 141120bk

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
141120.mq3	141120bk1	\([0, 0, 0, -49376712, 133521363416]\)	\(151591373397612544/32558203125\)	\(2859408167691600000000\)	\([2]\)	\(11796480\)	\(3.1119\)	\(\Gamma_0(N)\)-optimal
141120.mq2	141120bk2	\([0, 0, 0, -54889212, 101864178416]\)	\(13015144447800784/4341909875625\)	\(6101217571044535511040000\)	\([2, 2]\)	\(23592960\)	\(3.4585\)
141120.mq4	141120bk3	\([0, 0, 0, 159436788, 702577091216]\)	\(79743193254623804/84085819746075\)	\(-472626927417822919070515200\)	\([2]\)	\(47185920\)	\(3.8051\)
141120.mq1	141120bk4	\([0, 0, 0, -357415212, -2524908574384]\)	\(898353183174324196/29899176238575\)	\(168056348152820420940595200\)	\([2]\)	\(47185920\)	\(3.8051\)