Elliptic curve isogeny class with Cremona label 12600x (LMFDB label 12600.s)

• Label: 12600x
• Number of curves: $1$
• Conductor: $12600$
• CM: no
• Rank: $1$

Rank

The elliptic curve 12600x1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(5\)	\(1\)
\(7\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 - 3 T + 11 T^{2}\)	1.11.ad
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 + 4 T + 17 T^{2}\)	1.17.e
\(19\)	\( 1 + 2 T + 19 T^{2}\)	1.19.c
\(23\)	\( 1 + 9 T + 23 T^{2}\)	1.23.j
\(29\)	\( 1 - 7 T + 29 T^{2}\)	1.29.ah
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 12600x do not have complex multiplication.

Modular form 12600.2.a.x

Isogeny graph

Elliptic curves in class 12600x

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
12600.s1	12600x1	\([0, 0, 0, 1500, -537500]\)	\(1024/343\)	\(-125023500000000\)	\([]\)	\(28800\)	\(1.3841\)	\(\Gamma_0(N)\)-optimal