Elliptic curve isogeny class with LMFDB label 170352.bl (Cremona label 170352y)

• Label: 170352.bl
• Number of curves: $4$
• Conductor: $170352$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 170352.bl have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(7\)	\(1 + T\)
\(13\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 2 T + 5 T^{2}\)	1.5.c
\(11\)	\( 1 - 4 T + 11 T^{2}\)	1.11.ae
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 170352.bl do not have complex multiplication.

Modular form 170352.2.a.bl

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 170352.bl

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
170352.bl1	170352y3	\([0, 0, 0, -47613891, 126433153730]\)	\(828279937799497/193444524\)	\(2788072292043222073344\)	\([2]\)	\(12386304\)	\(3.1056\)
170352.bl2	170352y2	\([0, 0, 0, -3322371, 1486775810]\)	\(281397674377/96589584\)	\(1392123887933789896704\)	\([2, 2]\)	\(6193152\)	\(2.7590\)
170352.bl3	170352y1	\([0, 0, 0, -1375491, -603783934]\)	\(19968681097/628992\)	\(9065519823744663552\)	\([2]\)	\(3096576\)	\(2.4124\)	\(\Gamma_0(N)\)-optimal
170352.bl4	170352y4	\([0, 0, 0, 9819069, 10336221506]\)	\(7264187703863/7406095788\)	\(-106742388110923279024128\)	\([2]\)	\(12386304\)	\(3.1056\)