Elliptic curve isogeny class with LMFDB label 244608.f (Cremona label 244608f)

• Label: 244608.f
• Number of curves: $1$
• Conductor: $244608$
• CM: no
• Rank: $2$

Rank

The elliptic curve 244608.f1 has rank \(2\).

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 \(\mathbb{F}_p\)
\(5\)	\( 1 + 3 T + 5 T^{2}\)	1.5.d
\(11\)	\( 1 + 5 T + 11 T^{2}\)	1.11.f
\(17\)	\( 1 - 5 T + 17 T^{2}\)	1.17.af
\(19\)	\( 1 - 5 T + 19 T^{2}\)	1.19.af
\(23\)	\( 1 + T + 23 T^{2}\)	1.23.b
\(29\)	\( 1 - 9 T + 29 T^{2}\)	1.29.aj
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 244608.f do not have complex multiplication.

Modular form 244608.2.a.f

Elliptic curves in class 244608.f

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
244608.f1	244608f1	\([0, -1, 0, -412302, 115022286]\)	\(-514722176765024/80754929073\)	\(-1216094291265200256\)	\([]\)	\(5806080\)	\(2.1987\)	\(\Gamma_0(N)\)-optimal