Elliptic curve isogeny class with LMFDB label 13520.bf (Cremona label 13520bf)

• Label: 13520.bf
• Number of curves: $1$
• Conductor: $13520$
• CM: no
• Rank: $1$

Rank

The elliptic curve 13520.bf1 has rank \(1\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 - 3 T + 3 T^{2}\)	1.3.ad
\(7\)	\( 1 + 3 T + 7 T^{2}\)	1.7.d
\(11\)	\( 1 + 3 T + 11 T^{2}\)	1.11.d
\(17\)	\( 1 + 7 T + 17 T^{2}\)	1.17.h
\(19\)	\( 1 + T + 19 T^{2}\)	1.19.b
\(23\)	\( 1 - 7 T + 23 T^{2}\)	1.23.ah
\(29\)	\( 1 + 5 T + 29 T^{2}\)	1.29.f
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 13520.bf do not have complex multiplication.

Modular form 13520.2.a.bf

Elliptic curves in class 13520.bf

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
13520.bf1	13520bf1	\([0, 0, 0, -2197, -28561]\)	\(89856/25\)	\(326292288400\)	\([]\)	\(29952\)	\(0.91652\)	\(\Gamma_0(N)\)-optimal