Elliptic curve isogeny class with LMFDB label 340704.do (Cremona label 340704do)

• Label: 340704.do
• Number of curves: $1$
• Conductor: $340704$
• CM: no
• Rank: $2$

Rank

The elliptic curve 340704.do1 has rank \(2\).

L-function data

Bad L-factors:

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

Good L-factors:

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

See L-function page for more information

Complex multiplication

The elliptic curves in class 340704.do do not have complex multiplication.

Modular form 340704.2.a.do

Isogeny graph

Elliptic curves in class 340704.do

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
340704.do1	340704do1	\([0, 0, 0, -1034787, 551741398]\)	\(-30959144/15309\)	\(-60594678157832372736\)	\([]\)	\(8386560\)	\(2.5011\)	\(\Gamma_0(N)\)-optimal