Elliptic curve isogeny class with LMFDB label 34680.r (Cremona label 34680bj)

• Label: 34680.r
• Number of curves: $1$
• Conductor: $34680$
• CM: no
• Rank: $1$

Rank

The elliptic curve 34680.r1 has rank \(1\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 + 7 T^{2}\)	1.7.a
\(11\)	\( 1 + 5 T + 11 T^{2}\)	1.11.f
\(13\)	\( 1 - 4 T + 13 T^{2}\)	1.13.ae
\(19\)	\( 1 - 7 T + 19 T^{2}\)	1.19.ah
\(23\)	\( 1 - 6 T + 23 T^{2}\)	1.23.ag
\(29\)	\( 1 + 3 T + 29 T^{2}\)	1.29.d
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 34680.r do not have complex multiplication.

Modular form 34680.2.a.r

Elliptic curves in class 34680.r

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
34680.r1	34680bj1	\([0, -1, 0, -5145, 143757]\)	\(203622820864/28125\)	\(2080800000\)	\([]\)	\(34560\)	\(0.80547\)	\(\Gamma_0(N)\)-optimal