Elliptic curve isogeny class with Cremona label 214896bf (LMFDB label 214896.x)

• Label: 214896bf
• Number of curves: $1$
• Conductor: $214896$
• CM: no
• Rank: $1$

Rank

The elliptic curve 214896bf1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 + T\)
\(11\)	\(1\)
\(37\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - 2 T + 5 T^{2}\)	1.5.ac
\(7\)	\( 1 - 4 T + 7 T^{2}\)	1.7.ae
\(13\)	\( 1 + 13 T^{2}\)	1.13.a
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 - 6 T + 19 T^{2}\)	1.19.ag
\(23\)	\( 1 + 8 T + 23 T^{2}\)	1.23.i
\(29\)	\( 1 + 8 T + 29 T^{2}\)	1.29.i
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 214896bf do not have complex multiplication.

Modular form 214896.2.a.bf

Elliptic curves in class 214896bf

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
214896.x1	214896bf1	\([0, -1, 0, 37712, -6859136]\)	\(6755375/26973\)	\(-23682670990184448\)	\([]\)	\(1419264\)	\(1.8246\)	\(\Gamma_0(N)\)-optimal