Elliptic curve isogeny class with LMFDB label 8004.c (Cremona label 8004c)

• Label: 8004.c
• Number of curves: $1$
• Conductor: $8004$
• CM: no
• Rank: $1$

Rank

The elliptic curve 8004.c1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 - T\)
\(23\)	\(1 + T\)
\(29\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 2 T + 5 T^{2}\)	1.5.c
\(7\)	\( 1 - 3 T + 7 T^{2}\)	1.7.ad
\(11\)	\( 1 - 3 T + 11 T^{2}\)	1.11.ad
\(13\)	\( 1 - T + 13 T^{2}\)	1.13.ab
\(17\)	\( 1 + 5 T + 17 T^{2}\)	1.17.f
\(19\)	\( 1 + 2 T + 19 T^{2}\)	1.19.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 8004.c do not have complex multiplication.

Modular form 8004.2.a.c

Elliptic curves in class 8004.c

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
8004.c1	8004c1	\([0, 1, 0, -8414, 294297]\)	\(-4117777414120192/301956903\)	\(-4831310448\)	\([]\)	\(8208\)	\(0.90878\)	\(\Gamma_0(N)\)-optimal