Elliptic curve isogeny class with LMFDB label 193550.i (Cremona label 193550ce)

• Label: 193550.i
• Number of curves: $1$
• Conductor: $193550$
• CM: no
• Rank: $1$

Rank

The elliptic curve 193550.i1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 + T\)
\(5\)	\(1\)
\(7\)	\(1\)
\(79\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + T + 3 T^{2}\)	1.3.b
\(11\)	\( 1 + 3 T + 11 T^{2}\)	1.11.d
\(13\)	\( 1 + 4 T + 13 T^{2}\)	1.13.e
\(17\)	\( 1 + T + 17 T^{2}\)	1.17.b
\(19\)	\( 1 - 5 T + 19 T^{2}\)	1.19.af
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 193550.i do not have complex multiplication.

Modular form 193550.2.a.i

Elliptic curves in class 193550.i

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
193550.i1	193550ce1	\([1, 1, 0, 198425, -124412875]\)	\(18800144375/156574208\)	\(-7195624608200000000\)	\([]\)	\(3525120\)	\(2.2997\)	\(\Gamma_0(N)\)-optimal