Elliptic curve isogeny class with LMFDB label 17784.p (Cremona label 17784t)

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

Rank

The elliptic curve 17784.p1 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 \(\mathbb{F}_p\)
\(5\)	\( 1 - 2 T + 5 T^{2}\)	1.5.ac
\(7\)	\( 1 + 2 T + 7 T^{2}\)	1.7.c
\(11\)	\( 1 + 2 T + 11 T^{2}\)	1.11.c
\(17\)	\( 1 - 3 T + 17 T^{2}\)	1.17.ad
\(23\)	\( 1 - 3 T + 23 T^{2}\)	1.23.ad
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 17784.2.a.p

Elliptic curves in class 17784.p

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
17784.p1	17784t1	\([0, 0, 0, -939, 14627]\)	\(-7850060032/3381183\)	\(-39438118512\)	\([]\)	\(9216\)	\(0.74066\)	\(\Gamma_0(N)\)-optimal