Elliptic curve isogeny class with Cremona label 141610y (LMFDB label 141610.ck)

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

Rank

The elliptic curves in class 141610y 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.ab
\(11\)	\( 1 - 6 T + 11 T^{2}\)	1.11.ag
\(13\)	\( 1 - 4 T + 13 T^{2}\)	1.13.ae
\(19\)	\( 1 + 2 T + 19 T^{2}\)	1.19.c
\(23\)	\( 1 - 3 T + 23 T^{2}\)	1.23.ad
\(29\)	\( 1 - 3 T + 29 T^{2}\)	1.29.ad
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 141610y do not have complex multiplication.

Modular form 141610.2.a.y

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 141610y

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
141610.ck2	141610y1	\([1, 0, 0, 15889, -2041159]\)	\(375078431/1740800\)	\(-2058915325644800\)	\([]\)	\(663552\)	\(1.6208\)	\(\Gamma_0(N)\)-optimal
141610.ck1	141610y2	\([1, 0, 0, -145951, 61820905]\)	\(-290707016929/1228250000\)	\(-1452701487088250000\)	\([]\)	\(1990656\)	\(2.1701\)