Elliptic curve isogeny class with LMFDB label 206400.fw (Cremona label 206400gi)

• Label: 206400.fw
• Number of curves: $4$
• Conductor: $206400$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 206400.fw have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 - T\)
\(5\)	\(1\)
\(43\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 + 4 T + 7 T^{2}\)	1.7.e
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 - 6 T + 13 T^{2}\)	1.13.ag
\(17\)	\( 1 - 6 T + 17 T^{2}\)	1.17.ag
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 + 23 T^{2}\)	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 206400.fw do not have complex multiplication.

Modular form 206400.2.a.fw

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 206400.fw

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
206400.fw1	206400gi3	\([0, 1, 0, -25981633, 50964264863]\)	\(947094050118111698/20769216075\)	\(42535354521600000000\)	\([2]\)	\(15728640\)	\(2.8821\)
206400.fw2	206400gi2	\([0, 1, 0, -1681633, 736164863]\)	\(513591322675396/68238500625\)	\(69876224640000000000\)	\([2, 2]\)	\(7864320\)	\(2.5356\)
206400.fw3	206400gi1	\([0, 1, 0, -431633, -97585137]\)	\(34739908901584/4081640625\)	\(1044900000000000000\)	\([2]\)	\(3932160\)	\(2.1890\)	\(\Gamma_0(N)\)-optimal
206400.fw4	206400gi4	\([0, 1, 0, 2618367, 3888064863]\)	\(969360123836302/3748293231075\)	\(-7676504537241600000000\)	\([2]\)	\(15728640\)	\(2.8821\)