Elliptic curve isogeny class with Cremona label 17784j (LMFDB label 17784.e)

• Label: 17784j
• Number of curves: $1$
• Conductor: $17784$
• CM: no
• Rank: $1$

Rank

The elliptic curve 17784j1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(13\)	\(1 + T\)
\(19\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 5 T^{2}\)	1.5.a
\(7\)	\( 1 + 7 T^{2}\)	1.7.a
\(11\)	\( 1 - 4 T + 11 T^{2}\)	1.11.ae
\(17\)	\( 1 + 7 T + 17 T^{2}\)	1.17.h
\(23\)	\( 1 - T + 23 T^{2}\)	1.23.ab
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 17784j do not have complex multiplication.

Modular form 17784.2.a.j

Elliptic curves in class 17784j

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
17784.e1	17784j1	\([0, 0, 0, 309, -986]\)	\(59007258/41743\)	\(-2308220928\)	\([]\)	\(8832\)	\(0.48511\)	\(\Gamma_0(N)\)-optimal