Elliptic curve isogeny class with LMFDB label 213282.p (Cremona label 213282bm)

• Label: 213282.p
• Number of curves: $1$
• Conductor: $213282$
• CM: no
• Rank: $0$

Rank

The elliptic curve 213282.p1 has rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 + T\)
\(3\)	\(1\)
\(17\)	\(1\)
\(41\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - T + 5 T^{2}\)	1.5.ab
\(7\)	\( 1 + 3 T + 7 T^{2}\)	1.7.d
\(11\)	\( 1 + T + 11 T^{2}\)	1.11.b
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(19\)	\( 1 - 7 T + 19 T^{2}\)	1.19.ah
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 + 4 T + 29 T^{2}\)	1.29.e
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 213282.p do not have complex multiplication.

Modular form 213282.2.a.p

Elliptic curves in class 213282.p

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
213282.p1	213282bm1	\([1, -1, 0, -819, -9099]\)	\(-288568081/10496\)	\(-2211307776\)	\([]\)	\(103680\)	\(0.56453\)	\(\Gamma_0(N)\)-optimal