Elliptic curve isogeny class with Cremona label 171462l (LMFDB label 171462.q)

• Label: 171462l
• Number of curves: $2$
• Conductor: $171462$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 171462l have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 + T\)
\(3\)	\(1 - T\)
\(17\)	\(1 + T\)
\(41\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - 3 T + 5 T^{2}\)	1.5.ad
\(7\)	\( 1 - 3 T + 7 T^{2}\)	1.7.ad
\(11\)	\( 1 + 2 T + 11 T^{2}\)	1.11.c
\(13\)	\( 1 - 6 T + 13 T^{2}\)	1.13.ag
\(19\)	\( 1 + 8 T + 19 T^{2}\)	1.19.i
\(23\)	\( 1 + 8 T + 23 T^{2}\)	1.23.i
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 171462l do not have complex multiplication.

Modular form 171462.2.a.l

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 171462l

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
171462.q2	171462l1	\([1, 1, 1, 3340207481, 5567442730493]\)	\(867642675558875264539583/504925601466378092544\)	\(-2398449240914918396302744879104\)	\([]\)	\(446342400\)	\(4.5188\)	\(\Gamma_0(N)\)-optimal
171462.q1	171462l2	\([1, 1, 1, -43702510279, -3820421556509827]\)	\(-1943299427371886688757286977/202796948353367429302464\)	\(-963306644435188592560901918149824\)	\([]\)	\(1339027200\)	\(5.0681\)