Elliptic curve isogeny class with LMFDB label 122304.b (Cremona label 122304ft)

• Label: 122304.b
• Number of curves: $1$
• Conductor: $122304$
• CM: no
• Rank: $1$

Rank

The elliptic curve 122304.b1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 + T\)
\(7\)	\(1\)
\(13\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 4 T + 5 T^{2}\)	1.5.e
\(11\)	\( 1 + T + 11 T^{2}\)	1.11.b
\(17\)	\( 1 + 3 T + 17 T^{2}\)	1.17.d
\(19\)	\( 1 - T + 19 T^{2}\)	1.19.ab
\(23\)	\( 1 + 6 T + 23 T^{2}\)	1.23.g
\(29\)	\( 1 - 9 T + 29 T^{2}\)	1.29.aj
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 122304.b do not have complex multiplication.

Modular form 122304.2.a.b

Elliptic curves in class 122304.b

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
122304.b1	122304ft1	\([0, -1, 0, -11681665, 15751629601]\)	\(-2380771254001/69009408\)	\(-5110090880291331637248\)	\([]\)	\(12386304\)	\(2.9447\)	\(\Gamma_0(N)\)-optimal