Elliptic curve isogeny class with LMFDB label 340704.el (Cremona label 340704el)

• Label: 340704.el
• Number of curves: $4$
• Conductor: $340704$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 340704.el have rank \(0\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - 2 T + 5 T^{2}\)	1.5.ac
\(11\)	\( 1 - 4 T + 11 T^{2}\)	1.11.ae
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 + 8 T + 23 T^{2}\)	1.23.i
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 340704.el do not have complex multiplication.

Modular form 340704.2.a.el

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.

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 340704.el

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
340704.el1	340704el2	\([0, 0, 0, -756444, 252742880]\)	\(3321287488/7371\)	\(106236560434507776\)	\([2]\)	\(4128768\)	\(2.1497\)
340704.el2	340704el4	\([0, 0, 0, -657579, -204290242]\)	\(17454600584/93639\)	\(168699723282574848\)	\([2]\)	\(4128768\)	\(2.1497\)
340704.el3	340704el1	\([0, 0, 0, -64389, 834860]\)	\(131096512/74529\)	\(16783901040868416\)	\([2, 2]\)	\(2064384\)	\(1.8031\)	\(\Gamma_0(N)\)-optimal
340704.el4	340704el3	\([0, 0, 0, 255021, 6648122]\)	\(1018108216/599781\)	\(-1080563533678766592\)	\([2]\)	\(4128768\)	\(2.1497\)