Elliptic curve isogeny class with LMFDB label 17787.bc (Cremona label 17787ba)

• Label: 17787.bc
• Number of curves: $1$
• Conductor: $17787$
• CM: no
• Rank: $0$

Rank

The elliptic curve 17787.bc1 has rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(3\)	\(1 - T\)
\(7\)	\(1\)
\(11\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(2\)	\( 1 - 2 T + 2 T^{2}\)	1.2.ac
\(5\)	\( 1 + 3 T + 5 T^{2}\)	1.5.d
\(13\)	\( 1 - 4 T + 13 T^{2}\)	1.13.ae
\(17\)	\( 1 + T + 17 T^{2}\)	1.17.b
\(19\)	\( 1 - 2 T + 19 T^{2}\)	1.19.ac
\(23\)	\( 1 + 8 T + 23 T^{2}\)	1.23.i
\(29\)	\( 1 - 10 T + 29 T^{2}\)	1.29.ak
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 17787.bc do not have complex multiplication.

Modular form 17787.2.a.bc

Elliptic curves in class 17787.bc

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
17787.bc1	17787ba1	\([0, 1, 1, -34162, 938515]\)	\(495616/243\)	\(2161858403068749\)	\([]\)	\(168960\)	\(1.6358\)	\(\Gamma_0(N)\)-optimal