Elliptic curve isogeny class with Cremona label 17787l (LMFDB label 17787.c)

• Label: 17787l
• Number of curves: $1$
• Conductor: $17787$
• CM: no
• Rank: $1$

Rank

The elliptic curve 17787l1 has rank \(1\).

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 \(\mathbb{F}_p\)
\(2\)	\( 1 + T + 2 T^{2}\)	1.2.b
\(5\)	\( 1 + T + 5 T^{2}\)	1.5.b
\(13\)	\( 1 + 5 T + 13 T^{2}\)	1.13.f
\(17\)	\( 1 - 7 T + 17 T^{2}\)	1.17.ah
\(19\)	\( 1 - 6 T + 19 T^{2}\)	1.19.ag
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 - 9 T + 29 T^{2}\)	1.29.aj
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 17787.2.a.l

Elliptic curves in class 17787l

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
17787.c1	17787l1	\([0, -1, 1, -13834, 249402]\)	\(495616/243\)	\(143568569901141\)	\([]\)	\(107520\)	\(1.4098\)	\(\Gamma_0(N)\)-optimal