Elliptic curve isogeny class with LMFDB label 193200.ei (Cremona label 193200ga)

• Label: 193200.ei
• Number of curves: $1$
• Conductor: $193200$
• CM: no
• Rank: $1$

Rank

The elliptic curve 193200.ei1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 - T\)
\(5\)	\(1\)
\(7\)	\(1 + T\)
\(23\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 + T + 11 T^{2}\)	1.11.b
\(13\)	\( 1 - 6 T + 13 T^{2}\)	1.13.ag
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 + 7 T + 19 T^{2}\)	1.19.h
\(29\)	\( 1 + 10 T + 29 T^{2}\)	1.29.k
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 193200.ei do not have complex multiplication.

Modular form 193200.2.a.ei

Elliptic curves in class 193200.ei

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
193200.ei1	193200ga1	\([0, 1, 0, 167, -57037]\)	\(128000/352107\)	\(-1408428000000\)	\([]\)	\(322560\)	\(1.0101\)	\(\Gamma_0(N)\)-optimal