Elliptic curve isogeny class with LMFDB label 344760.bg (Cremona label 344760bg)

• Label: 344760.bg
• Number of curves: $1$
• Conductor: $344760$
• CM: no
• Rank: $1$

Rank

The elliptic curve 344760.bg1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 + T\)
\(5\)	\(1 - T\)
\(13\)	\(1\)
\(17\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 - 3 T + 7 T^{2}\)	1.7.ad
\(11\)	\( 1 + 3 T + 11 T^{2}\)	1.11.d
\(19\)	\( 1 - 5 T + 19 T^{2}\)	1.19.af
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 + 5 T + 29 T^{2}\)	1.29.f
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 344760.bg do not have complex multiplication.

Modular form 344760.2.a.bg

Elliptic curves in class 344760.bg

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
344760.bg1	344760bg1	\([0, -1, 0, 1291780, -2792217975]\)	\(3086803246205696/45384521484375\)	\(-3504998668183593750000\)	\([]\)	\(18869760\)	\(2.8147\)	\(\Gamma_0(N)\)-optimal