Elliptic curve isogeny class with Cremona label 122a (LMFDB label 122.a)

• Label: 122a
• Number of curves: $1$
• Conductor: $122$
• CM: no
• Rank: $1$

Rank

The elliptic curve 122a1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 + T\)
\(61\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + 2 T + 3 T^{2}\)	1.3.c
\(5\)	\( 1 - T + 5 T^{2}\)	1.5.ab
\(7\)	\( 1 + 5 T + 7 T^{2}\)	1.7.f
\(11\)	\( 1 + 3 T + 11 T^{2}\)	1.11.d
\(13\)	\( 1 + 3 T + 13 T^{2}\)	1.13.d
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 - 5 T + 23 T^{2}\)	1.23.af
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 122a do not have complex multiplication.

Modular form 122.2.a.a

Elliptic curves in class 122a

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
122.a1	122a1	\([1, 0, 1, 2, 0]\)	\(1685159/976\)	\(-976\)	\([]\)	\(8\)	\(-0.73692\)	\(\Gamma_0(N)\)-optimal