Elliptic curve isogeny class with Cremona label 348480qx (LMFDB label 348480.qx)

• Label: 348480qx
• Number of curves: $4$
• Conductor: $348480$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 348480qx have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(5\)	\(1 - T\)
\(11\)	\(1\)

Good L-factors:

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

See L-function page for more information

Complex multiplication

The elliptic curves in class 348480qx do not have complex multiplication.

Modular form 348480.2.a.qx

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 348480qx

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
348480.qx3	348480qx1	\([0, 0, 0, -1569612, -638262416]\)	\(1263214441/211200\)	\(71501882340881203200\)	\([2]\)	\(11796480\)	\(2.5308\)	\(\Gamma_0(N)\)-optimal
348480.qx2	348480qx2	\([0, 0, 0, -7145292, 6746168176]\)	\(119168121961/10890000\)	\(3686815808201687040000\)	\([2, 2]\)	\(23592960\)	\(2.8774\)
348480.qx1	348480qx3	\([0, 0, 0, -111689292, 454319940976]\)	\(455129268177961/4392300\)	\(1487015709308013772800\)	\([2]\)	\(47185920\)	\(3.2240\)
348480.qx4	348480qx4	\([0, 0, 0, 8187828, 31775953264]\)	\(179310732119/1392187500\)	\(-471325884571238400000000\)	\([2]\)	\(47185920\)	\(3.2240\)