Elliptic curve isogeny class with LMFDB label 17136.s (Cremona label 17136i)

• Label: 17136.s
• Number of curves: $1$
• Conductor: $17136$
• CM: no
• Rank: $1$

Rank

The elliptic curve 17136.s1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(7\)	\(1 - T\)
\(17\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + T + 5 T^{2}\)	1.5.b
\(11\)	\( 1 + 3 T + 11 T^{2}\)	1.11.d
\(13\)	\( 1 + T + 13 T^{2}\)	1.13.b
\(19\)	\( 1 + 6 T + 19 T^{2}\)	1.19.g
\(23\)	\( 1 - 6 T + 23 T^{2}\)	1.23.ag
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 17136.s do not have complex multiplication.

Modular form 17136.2.a.s

Elliptic curves in class 17136.s

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
17136.s1	17136i1	\([0, 0, 0, -3, -23326]\)	\(-2/157437\)	\(-235052181504\)	\([]\)	\(13824\)	\(0.86081\)	\(\Gamma_0(N)\)-optimal