Elliptic curve isogeny class with LMFDB label 8112.n (Cremona label 8112c)

• Label: 8112.n
• Number of curves: $1$
• Conductor: $8112$
• CM: no
• Rank: $1$

Elliptic curves in class 8112.n

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
8112.n1	8112c1	\([0, -1, 0, 8056, -284064]\)	\(69212/81\)	\(-67659968922624\)	\([]\)	\(19968\)	\(1.3401\)	\(\Gamma_0(N)\)-optimal

Rank

The elliptic curve 8112.n1 has rank \(1\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - 3 T + 5 T^{2}\)	1.5.ad
\(7\)	\( 1 + 7 T^{2}\)	1.7.a
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(17\)	\( 1 + T + 17 T^{2}\)	1.17.b
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 - 3 T + 29 T^{2}\)	1.29.ad
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 8112.n do not have complex multiplication.

Modular form 8112.2.a.n