Elliptic curve isogeny class with Cremona label 83205x (LMFDB label 83205.a)

• Label: 83205x
• Number of curves: $1$
• Conductor: $83205$
• CM: no
• Rank: $0$

Rank

The elliptic curve 83205x1 has rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(3\)	\(1\)
\(5\)	\(1 - T\)
\(43\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(2\)	\( 1 - 2 T + 2 T^{2}\)	1.2.ac
\(7\)	\( 1 + 7 T^{2}\)	1.7.a
\(11\)	\( 1 + 5 T + 11 T^{2}\)	1.11.f
\(13\)	\( 1 - T + 13 T^{2}\)	1.13.ab
\(17\)	\( 1 + 5 T + 17 T^{2}\)	1.17.f
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 + 3 T + 23 T^{2}\)	1.23.d
\(29\)	\( 1 + 8 T + 29 T^{2}\)	1.29.i
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 83205x do not have complex multiplication.

Modular form 83205.2.a.x

Isogeny graph

Elliptic curves in class 83205x

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
83205.a1	83205x1	\([0, 0, 1, -299543547, -1995437208780]\)	\(-645008376471556096/783675\)	\(-3611388862632879675\)	\([]\)	\(17031168\)	\(3.2724\)	\(\Gamma_0(N)\)-optimal