Elliptic curve isogeny class with Cremona label 17424bz (LMFDB label 17424.i)

• Label: 17424bz
• Number of curves: $4$
• Conductor: $17424$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 17424bz have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(11\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - 3 T + 5 T^{2}\)	1.5.ad
\(7\)	\( 1 + 2 T + 7 T^{2}\)	1.7.c
\(13\)	\( 1 + 13 T^{2}\)	1.13.a
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 - T + 23 T^{2}\)	1.23.ab
\(29\)	\( 1 + 8 T + 29 T^{2}\)	1.29.i
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 17424bz do not have complex multiplication.

Modular form 17424.2.a.bz

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 17424bz

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
17424.i4	17424bz1	\([0, 0, 0, -35211, -45254]\)	\(912673/528\)	\(2793042278940672\)	\([2]\)	\(92160\)	\(1.6533\)	\(\Gamma_0(N)\)-optimal
17424.i2	17424bz2	\([0, 0, 0, -383691, 91186810]\)	\(1180932193/4356\)	\(23042598801260544\)	\([2, 2]\)	\(184320\)	\(1.9999\)
17424.i1	17424bz3	\([0, 0, 0, -6133611, 5846856730]\)	\(4824238966273/66\)	\(349130284867584\)	\([4]\)	\(368640\)	\(2.3464\)
17424.i3	17424bz4	\([0, 0, 0, -209451, 174368986]\)	\(-192100033/2371842\)	\(-12546695047286366208\)	\([2]\)	\(368640\)	\(2.3464\)