Elliptic curve isogeny class with LMFDB label 17424.by (Cremona label 17424bw)

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

Rank

The elliptic curves in class 17424.by 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 \(\mathbb{F}_p\)
\(5\)	\( 1 - 2 T + 5 T^{2}\)	1.5.ac
\(7\)	\( 1 - 4 T + 7 T^{2}\)	1.7.ae
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 - 8 T + 23 T^{2}\)	1.23.ai
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 17424.2.a.by

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 17424.by

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
17424.by1	17424bw3	\([0, 0, 0, -2552979, -1568527598]\)	\(347873904937/395307\)	\(2091115841214394368\)	\([2]\)	\(368640\)	\(2.4288\)
17424.by2	17424bw2	\([0, 0, 0, -200739, -10874270]\)	\(169112377/88209\)	\(466612625725526016\)	\([2, 2]\)	\(184320\)	\(2.0822\)
17424.by3	17424bw1	\([0, 0, 0, -113619, 14617042]\)	\(30664297/297\)	\(1571086281904128\)	\([2]\)	\(92160\)	\(1.7356\)	\(\Gamma_0(N)\)-optimal
17424.by4	17424bw4	\([0, 0, 0, 757581, -84664910]\)	\(9090072503/5845851\)	\(-30923691286718951424\)	\([2]\)	\(368640\)	\(2.4288\)