Elliptic curve isogeny class with Cremona label 9996a (LMFDB label 9996.d)

• Label: 9996a
• Number of curves: $1$
• Conductor: $9996$
• CM: no
• Rank: $0$

Rank

The elliptic curve 9996a1 has rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 + T\)
\(7\)	\(1\)
\(17\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 2 T + 5 T^{2}\)	1.5.c
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(19\)	\( 1 + 6 T + 19 T^{2}\)	1.19.g
\(23\)	\( 1 - 8 T + 23 T^{2}\)	1.23.ai
\(29\)	\( 1 + 4 T + 29 T^{2}\)	1.29.e
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 9996a do not have complex multiplication.

Modular form 9996.2.a.a

Elliptic curves in class 9996a

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
9996.d1	9996a1	\([0, -1, 0, -186020, 11030664]\)	\(482370434896/243931419\)	\(359991318574750464\)	\([]\)	\(105840\)	\(2.0613\)	\(\Gamma_0(N)\)-optimal