Elliptic curve isogeny class with LMFDB label 241200.gx (Cremona label 241200gx)

• Label: 241200.gx
• Number of curves: $1$
• Conductor: $241200$
• CM: no
• Rank: $1$

Rank

The elliptic curve 241200.gx1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(5\)	\(1\)
\(67\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 - 5 T + 7 T^{2}\)	1.7.af
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 - 6 T + 23 T^{2}\)	1.23.ag
\(29\)	\( 1 + 9 T + 29 T^{2}\)	1.29.j
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 241200.gx do not have complex multiplication.

Modular form 241200.2.a.gx

Elliptic curves in class 241200.gx

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
241200.gx1	241200gx1	\([0, 0, 0, -271425, 54428875]\)	\(-12134048168704/209375\)	\(-38158593750000\)	\([]\)	\(1555200\)	\(1.7350\)	\(\Gamma_0(N)\)-optimal