Elliptic curve isogeny class with LMFDB label 346800.ep (Cremona label 346800ep)

• Label: 346800.ep
• Number of curves: $4$
• Conductor: $346800$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 346800.ep have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 + T\)
\(5\)	\(1\)
\(17\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 - 2 T + 7 T^{2}\)	1.7.ac
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 - 6 T + 13 T^{2}\)	1.13.ag
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 + 6 T + 23 T^{2}\)	1.23.g
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 346800.ep do not have complex multiplication.

Modular form 346800.2.a.ep

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 5 & 10 \\ 2 & 1 & 10 & 5 \\ 5 & 10 & 1 & 2 \\ 10 & 5 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 346800.ep

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
346800.ep1	346800ep4	\([0, -1, 0, -8437808, 9163778112]\)	\(211293405175481/6973568802\)	\(2192713185550464000000\)	\([2]\)	\(19660800\)	\(2.8681\)
346800.ep2	346800ep3	\([0, -1, 0, -8369808, 9322898112]\)	\(206226044828441/236196\)	\(74267580672000000\)	\([2]\)	\(9830400\)	\(2.5216\)
346800.ep3	346800ep2	\([0, -1, 0, -1161808, -481613888]\)	\(551569744601/2592\)	\(815007744000000\)	\([2]\)	\(3932160\)	\(2.0634\)
346800.ep4	346800ep1	\([0, -1, 0, -73808, -7245888]\)	\(141420761/9216\)	\(2897805312000000\)	\([2]\)	\(1966080\)	\(1.7168\)	\(\Gamma_0(N)\)-optimal