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

• Label: 348480.hz
• Number of curves: $4$
• Conductor: $348480$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 348480.hz have rank \(1\).

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
\(13\)	\( 1 + 4 T + 13 T^{2}\)	1.13.e
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(19\)	\( 1 - 2 T + 19 T^{2}\)	1.19.ac
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 348480.2.a.hz

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.

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 348480.hz

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
348480.hz1	348480hz4	\([0, 0, 0, -6779388, -3690660688]\)	\(1628514404944/664335375\)	\(14056945377052317696000\)	\([2]\)	\(26542080\)	\(2.9474\)
348480.hz2	348480hz2	\([0, 0, 0, -3120348, 2121358448]\)	\(158792223184/16335\)	\(345638982018908160\)	\([2]\)	\(8847360\)	\(2.3981\)
348480.hz3	348480hz1	\([0, 0, 0, -180048, 38449928]\)	\(-488095744/200475\)	\(-265120810071321600\)	\([2]\)	\(4423680\)	\(2.0516\)	\(\Gamma_0(N)\)-optimal
348480.hz4	348480hz3	\([0, 0, 0, 1388112, -420393688]\)	\(223673040896/187171875\)	\(-247527916810416000000\)	\([2]\)	\(13271040\)	\(2.6009\)