Elliptic curve isogeny class with LMFDB label 141120.ie (Cremona label 141120b)

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

Rank

The elliptic curves in class 141120.ie 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 \(\mathbb{F}_p\)
\(11\)	\( 1 + 6 T + 11 T^{2}\)	1.11.g
\(13\)	\( 1 + 4 T + 13 T^{2}\)	1.13.e
\(17\)	\( 1 - 6 T + 17 T^{2}\)	1.17.ag
\(19\)	\( 1 + 2 T + 19 T^{2}\)	1.19.c
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 141120.2.a.ie

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.

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 141120.ie

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
141120.ie1	141120b3	\([0, 0, 0, -531552, 137773496]\)	\(189123395584/16078125\)	\(1412053416144000000\)	\([2]\)	\(2654208\)	\(2.2240\)
141120.ie2	141120b1	\([0, 0, 0, -108192, -13662376]\)	\(1594753024/4725\)	\(414970799846400\)	\([2]\)	\(884736\)	\(1.6747\)	\(\Gamma_0(N)\)-optimal
141120.ie3	141120b2	\([0, 0, 0, -64092, -24899056]\)	\(-20720464/178605\)	\(-250974339747102720\)	\([2]\)	\(1769472\)	\(2.0213\)
141120.ie4	141120b4	\([0, 0, 0, 570948, 634780496]\)	\(14647977776/132355125\)	\(-185984379547158528000\)	\([2]\)	\(5308416\)	\(2.5706\)