Elliptic curve isogeny class with LMFDB label 141610.ci (Cremona label 141610u)

• Label: 141610.ci
• Number of curves: $4$
• Conductor: $141610$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 141610.ci 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 \(\mathbb{F}_p\)
\(3\)	\( 1 + 3 T^{2}\)	1.3.a
\(11\)	\( 1 - 4 T + 11 T^{2}\)	1.11.ae
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(19\)	\( 1 - 8 T + 19 T^{2}\)	1.19.ai
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 141610.2.a.ci

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.

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 141610.ci

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
141610.ci1	141610u4	\([1, -1, 1, -19557016303, -1052688777516169]\)	\(291306206119284545407569/101150000000\)	\(287241810511673150000000\)	\([2]\)	\(148635648\)	\(4.2948\)
141610.ci2	141610u3	\([1, -1, 1, -1449062383, -9922199963273]\)	\(118495863754334673489/53596139570691200\)	\(152200219147025890272340227200\)	\([2]\)	\(148635648\)	\(4.2948\)
141610.ci3	141610u2	\([1, -1, 1, -1222486383, -16443147873673]\)	\(71149857462630609489/41907496960000\)	\(119007269409815507445760000\)	\([2, 2]\)	\(74317824\)	\(3.9482\)
141610.ci4	141610u1	\([1, -1, 1, -62417263, -353917234569]\)	\(-9470133471933009/13576123187200\)	\(-38552943193483287671603200\)	\([2]\)	\(37158912\)	\(3.6016\)	\(\Gamma_0(N)\)-optimal