Elliptic curve isogeny class with Cremona label 12870bp (LMFDB label 12870.bm)

• Label: 12870bp
• Number of curves: $1$
• Conductor: $12870$
• CM: no
• Rank: $0$

Rank

The elliptic curve 12870bp1 has rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(3\)	\(1\)
\(5\)	\(1 + T\)
\(11\)	\(1 - T\)
\(13\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 - 2 T + 7 T^{2}\)	1.7.ac
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 12870bp do not have complex multiplication.

Modular form 12870.2.a.bp

Elliptic curves in class 12870bp

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
12870.bm1	12870bp1	\([1, -1, 1, -9628403, 27433323987]\)	\(-135412551115258010417641/367535633653760000000\)	\(-267933476933591040000000\)	\([]\)	\(1532160\)	\(3.1828\)	\(\Gamma_0(N)\)-optimal