Elliptic curve isogeny class with LMFDB label 141120.ek (Cremona label 141120pp)

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

Rank

The elliptic curves in class 141120.ek 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
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 - 2 T + 19 T^{2}\)	1.19.ac
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 141120.2.a.ek

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.ek

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
141120.ek1	141120pp3	\([0, 0, 0, -1317708, 510169968]\)	\(416832723/56000\)	\(33994407923417088000\)	\([2]\)	\(2654208\)	\(2.4752\)
141120.ek2	141120pp1	\([0, 0, 0, -329868, -72831248]\)	\(4767078987/6860\)	\(5712366214840320\)	\([2]\)	\(884736\)	\(1.9259\)	\(\Gamma_0(N)\)-optimal
141120.ek3	141120pp2	\([0, 0, 0, -235788, -115242512]\)	\(-1740992427/5882450\)	\(-4898354029225574400\)	\([2]\)	\(1769472\)	\(2.2725\)
141120.ek4	141120pp4	\([0, 0, 0, 2069172, 2700803952]\)	\(1613964717/6125000\)	\(-3718138366623744000000\)	\([2]\)	\(5308416\)	\(2.8218\)