Elliptic curve isogeny class with LMFDB label 49725.n (Cremona label 49725g)

• Label: 49725.n
• Number of curves: $1$
• Conductor: $49725$
• CM: no
• Rank: $1$

Rank

The elliptic curve 49725.n1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(3\)	\(1\)
\(5\)	\(1\)
\(13\)	\(1 + T\)
\(17\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(2\)	\( 1 + 2 T^{2}\)	1.2.a
\(7\)	\( 1 + 2 T + 7 T^{2}\)	1.7.c
\(11\)	\( 1 + 2 T + 11 T^{2}\)	1.11.c
\(19\)	\( 1 - 2 T + 19 T^{2}\)	1.19.ac
\(23\)	\( 1 - 6 T + 23 T^{2}\)	1.23.ag
\(29\)	\( 1 - 5 T + 29 T^{2}\)	1.29.af
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 49725.n do not have complex multiplication.

Modular form 49725.2.a.n

Elliptic curves in class 49725.n

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
49725.n1	49725g1	\([0, 0, 1, -1200, 18531]\)	\(-16777216/3315\)	\(-37759921875\)	\([]\)	\(32256\)	\(0.75258\)	\(\Gamma_0(N)\)-optimal