Elliptic curve isogeny class with Cremona label 206400cl (LMFDB label 206400.kg)

• Label: 206400cl
• Number of curves: $2$
• Conductor: $206400$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 206400cl 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 \(\mathbb{F}_p\)
\(7\)	\( 1 + 7 T^{2}\)	1.7.a
\(11\)	\( 1 + 3 T + 11 T^{2}\)	1.11.d
\(13\)	\( 1 + T + 13 T^{2}\)	1.13.b
\(17\)	\( 1 - 6 T + 17 T^{2}\)	1.17.ag
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 - 7 T + 23 T^{2}\)	1.23.ah
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 206400cl do not have complex multiplication.

Modular form 206400.2.a.cl

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 206400cl

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
206400.kg1	206400cl1	\([0, 1, 0, -36033, -2591937]\)	\(1263214441/29025\)	\(118886400000000\)	\([2]\)	\(884736\)	\(1.4871\)	\(\Gamma_0(N)\)-optimal
206400.kg2	206400cl2	\([0, 1, 0, 3967, -7991937]\)	\(1685159/6739605\)	\(-27605422080000000\)	\([2]\)	\(1769472\)	\(1.8337\)