Elliptic curve isogeny class with Cremona label 17472cr (LMFDB label 17472.ch)

• Label: 17472cr
• Number of curves: $2$
• Conductor: $17472$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 17472cr have rank \(0\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - T + 5 T^{2}\)	1.5.ab
\(11\)	\( 1 - 2 T + 11 T^{2}\)	1.11.ac
\(17\)	\( 1 + 4 T + 17 T^{2}\)	1.17.e
\(19\)	\( 1 + 3 T + 19 T^{2}\)	1.19.d
\(23\)	\( 1 + 9 T + 23 T^{2}\)	1.23.j
\(29\)	\( 1 - T + 29 T^{2}\)	1.29.ab
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 17472cr do not have complex multiplication.

Modular form 17472.2.a.cr

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 17472cr

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
17472.ch2	17472cr1	\([0, 1, 0, -41293, -3329245]\)	\(-7604375980288000/236743082667\)	\(-242424916651008\)	\([2]\)	\(61440\)	\(1.5369\)	\(\Gamma_0(N)\)-optimal
17472.ch1	17472cr2	\([0, 1, 0, -665553, -209210193]\)	\(1989996724085074000/1843096437\)	\(30197292023808\)	\([2]\)	\(122880\)	\(1.8835\)