Elliptic curve isogeny class with LMFDB label 178464.n (Cremona label 178464ci)

• Label: 178464.n
• Number of curves: $1$
• Conductor: $178464$
• CM: no
• Rank: $1$

Rank

The elliptic curve 178464.n1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 + T\)
\(11\)	\(1 + T\)
\(13\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 5 T^{2}\)	1.5.a
\(7\)	\( 1 + 3 T + 7 T^{2}\)	1.7.d
\(17\)	\( 1 + 8 T + 17 T^{2}\)	1.17.i
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 + 6 T + 23 T^{2}\)	1.23.g
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 178464.n do not have complex multiplication.

Modular form 178464.2.a.n

Elliptic curves in class 178464.n

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
178464.n1	178464ci1	\([0, -1, 0, 1201027, 1111083765]\)	\(57342272000/192913083\)	\(-644567565459139964928\)	\([]\)	\(7527936\)	\(2.6760\)	\(\Gamma_0(N)\)-optimal