Elliptic curve isogeny class with LMFDB label 141120.mr (Cremona label 141120jk)

• Label: 141120.mr
• Number of curves: $4$
• Conductor: $141120$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 141120.mr have rank \(0\).

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
\(13\)	\( 1 - 6 T + 13 T^{2}\)	1.13.ag
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 141120.2.a.mr

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 LMFDB 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 LMFDB labels.

Elliptic curves in class 141120.mr

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
141120.mr1	141120jk3	\([0, 0, 0, -357415212, 2524908574384]\)	\(898353183174324196/29899176238575\)	\(168056348152820420940595200\)	\([2]\)	\(47185920\)	\(3.8051\)
141120.mr2	141120jk2	\([0, 0, 0, -54889212, -101864178416]\)	\(13015144447800784/4341909875625\)	\(6101217571044535511040000\)	\([2, 2]\)	\(23592960\)	\(3.4585\)
141120.mr3	141120jk1	\([0, 0, 0, -49376712, -133521363416]\)	\(151591373397612544/32558203125\)	\(2859408167691600000000\)	\([2]\)	\(11796480\)	\(3.1119\)	\(\Gamma_0(N)\)-optimal
141120.mr4	141120jk4	\([0, 0, 0, 159436788, -702577091216]\)	\(79743193254623804/84085819746075\)	\(-472626927417822919070515200\)	\([2]\)	\(47185920\)	\(3.8051\)