Elliptic curve isogeny class with Cremona label 141610n (LMFDB label 141610.cc)

• Label: 141610n
• Number of curves: $2$
• Conductor: $141610$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 141610n have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 + T\)
\(5\)	\(1 + T\)
\(7\)	\(1\)
\(17\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + T + 3 T^{2}\)	1.3.b
\(11\)	\( 1 - 3 T + 11 T^{2}\)	1.11.ad
\(13\)	\( 1 - 5 T + 13 T^{2}\)	1.13.af
\(19\)	\( 1 - 2 T + 19 T^{2}\)	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 141610n do not have complex multiplication.

Modular form 141610.2.a.n

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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 141610n

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
141610.cc2	141610n1	\([1, 1, 1, 778560, 700896097]\)	\(375078431/1740800\)	\(-242229329146785075200\)	\([]\)	\(4644864\)	\(2.5937\)	\(\Gamma_0(N)\)-optimal
141610.cc1	141610n2	\([1, 1, 1, -7151600, -21211722015]\)	\(-290707016929/1228250000\)	\(-170908877254445524250000\)	\([]\)	\(13934592\)	\(3.1431\)