Elliptic curve isogeny class with Cremona label 27200h (LMFDB label 27200.s)

• Label: 27200h
• Number of curves: $1$
• Conductor: $27200$
• CM: no
• Rank: $1$

Rank

The elliptic curve 27200h1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(5\)	\(1\)
\(17\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + 2 T + 3 T^{2}\)	1.3.c
\(7\)	\( 1 + 2 T + 7 T^{2}\)	1.7.c
\(11\)	\( 1 + 6 T + 11 T^{2}\)	1.11.g
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(19\)	\( 1 + 8 T + 19 T^{2}\)	1.19.i
\(23\)	\( 1 - 6 T + 23 T^{2}\)	1.23.ag
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 27200h do not have complex multiplication.

Modular form 27200.2.a.h

Elliptic curves in class 27200h

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
27200.s1	27200h1	\([0, -1, 0, -33, -20063]\)	\(-2/85\)	\(-174080000000\)	\([]\)	\(18432\)	\(0.83579\)	\(\Gamma_0(N)\)-optimal