Elliptic curve isogeny class with LMFDB label 271680.bd (Cremona label 271680bd)

• Label: 271680.bd
• Number of curves: $1$
• Conductor: $271680$
• CM: no
• Rank: $1$

Rank

The elliptic curve 271680.bd1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 - T\)
\(5\)	\(1 + T\)
\(283\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 + 3 T + 7 T^{2}\)	1.7.d
\(11\)	\( 1 - 3 T + 11 T^{2}\)	1.11.ad
\(13\)	\( 1 - 7 T + 13 T^{2}\)	1.13.ah
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 + 3 T + 23 T^{2}\)	1.23.d
\(29\)	\( 1 + 3 T + 29 T^{2}\)	1.29.d
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 271680.bd do not have complex multiplication.

Modular form 271680.2.a.bd

Isogeny graph

Elliptic curves in class 271680.bd

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
271680.bd1	271680bd1	\([0, 1, 0, -2721, 81855]\)	\(-8502154921/6367500\)	\(-1669201920000\)	\([]\)	\(466944\)	\(1.0445\)	\(\Gamma_0(N)\)-optimal