Elliptic curve isogeny class with Cremona label 141570i (LMFDB label 141570.ea)

• Label: 141570i
• Number of curves: $4$
• Conductor: $141570$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 141570i have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 + T\)
\(3\)	\(1\)
\(5\)	\(1 + T\)
\(11\)	\(1\)
\(13\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 + 2 T + 7 T^{2}\)	1.7.c
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 - T + 23 T^{2}\)	1.23.ab
\(29\)	\( 1 + 4 T + 29 T^{2}\)	1.29.e
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 141570i do not have complex multiplication.

Modular form 141570.2.a.i

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 141570i

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
141570.ea3	141570i1	\([1, -1, 1, -6557, 1313381]\)	\(-24137569/561600\)	\(-725288411390400\)	\([2]\)	\(552960\)	\(1.5322\)	\(\Gamma_0(N)\)-optimal
141570.ea2	141570i2	\([1, -1, 1, -224357, 40778741]\)	\(967068262369/4928040\)	\(6364405809950760\)	\([2]\)	\(1105920\)	\(1.8788\)
141570.ea4	141570i3	\([1, -1, 1, 58783, -34675891]\)	\(17394111071/411937500\)	\(-532004086479937500\)	\([2]\)	\(1658880\)	\(2.0815\)
141570.ea1	141570i4	\([1, -1, 1, -1302467, -542694391]\)	\(189208196468929/10860320250\)	\(14025755735957072250\)	\([2]\)	\(3317760\)	\(2.4281\)