Elliptic curve isogeny class with LMFDB label 17200.b (Cremona label 17200u)

• Label: 17200.b
• Number of curves: $1$
• Conductor: $17200$
• CM: no
• Rank: $0$

Rank

The elliptic curve 17200.b1 has rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(5\)	\(1\)
\(43\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + 3 T + 3 T^{2}\)	1.3.d
\(7\)	\( 1 + 2 T + 7 T^{2}\)	1.7.c
\(11\)	\( 1 - T + 11 T^{2}\)	1.11.ab
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 - 3 T + 17 T^{2}\)	1.17.ad
\(19\)	\( 1 + T + 19 T^{2}\)	1.19.b
\(23\)	\( 1 - 2 T + 23 T^{2}\)	1.23.ac
\(29\)	\( 1 - 4 T + 29 T^{2}\)	1.29.ae
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 17200.b do not have complex multiplication.

Modular form 17200.2.a.b

Isogeny graph

Elliptic curves in class 17200.b

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
17200.b1	17200u1	\([0, 0, 0, -194515, -33020270]\)	\(-7948461006944145/60588032\)	\(-6204214476800\)	\([]\)	\(103680\)	\(1.6294\)	\(\Gamma_0(N)\)-optimal