Elliptic curve isogeny class with Cremona label 141120ce (LMFDB label 141120.pd)

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

Rank

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

See L-function page for more information

Complex multiplication

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

Modular form 141120.2.a.ce

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 141120ce

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
141120.pd3	141120ce1	\([0, 0, 0, -8967, 326536]\)	\(14526784/15\)	\(82335476160\)	\([2]\)	\(196608\)	\(1.0124\)	\(\Gamma_0(N)\)-optimal
141120.pd2	141120ce2	\([0, 0, 0, -11172, 153664]\)	\(438976/225\)	\(79042057113600\)	\([2, 2]\)	\(393216\)	\(1.3590\)
141120.pd4	141120ce3	\([0, 0, 0, 41748, 1190896]\)	\(2863288/1875\)	\(-5269470474240000\)	\([2]\)	\(786432\)	\(1.7056\)
141120.pd1	141120ce4	\([0, 0, 0, -99372, -11947376]\)	\(38614472/405\)	\(1138205622435840\)	\([2]\)	\(786432\)	\(1.7056\)