Elliptic curve isogeny class with LMFDB label 126400.co (Cremona label 126400cf)

• Label: 126400.co
• Number of curves: $2$
• Conductor: $126400$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 126400.co have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(5\)	\(1\)
\(79\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 - 2 T + 3 T^{2}\)	1.3.ac
\(7\)	\( 1 - 2 T + 7 T^{2}\)	1.7.ac
\(11\)	\( 1 - 4 T + 11 T^{2}\)	1.11.ae
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 + 4 T + 17 T^{2}\)	1.17.e
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 126400.co do not have complex multiplication.

Modular form 126400.2.a.co

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 126400.co

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
126400.co1	126400cf2	\([0, -1, 0, -8033, 55937]\)	\(55990084/31205\)	\(31953920000000\)	\([2]\)	\(245760\)	\(1.2816\)
126400.co2	126400cf1	\([0, -1, 0, 1967, 5937]\)	\(3286064/1975\)	\(-505600000000\)	\([2]\)	\(122880\)	\(0.93502\)	\(\Gamma_0(N)\)-optimal