Elliptic curve isogeny class with LMFDB label 154804.a (Cremona label 154804a)

• Label: 154804.a
• Number of curves: $1$
• Conductor: $154804$
• CM: no
• Rank: $1$

Rank

The elliptic curve 154804.a1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(13\)	\(1\)
\(229\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + 3 T + 3 T^{2}\)	1.3.d
\(5\)	\( 1 - 3 T + 5 T^{2}\)	1.5.ad
\(7\)	\( 1 - 4 T + 7 T^{2}\)	1.7.ae
\(11\)	\( 1 - 3 T + 11 T^{2}\)	1.11.ad
\(17\)	\( 1 + 7 T + 17 T^{2}\)	1.17.h
\(19\)	\( 1 - 5 T + 19 T^{2}\)	1.19.af
\(23\)	\( 1 + 6 T + 23 T^{2}\)	1.23.g
\(29\)	\( 1 - 8 T + 29 T^{2}\)	1.29.ai
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 154804.a do not have complex multiplication.

Modular form 154804.2.a.a

Elliptic curves in class 154804.a

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
154804.a1	154804a1	\([0, 0, 0, -676, 2197]\)	\(442368/229\)	\(17685428176\)	\([]\)	\(285120\)	\(0.65835\)	\(\Gamma_0(N)\)-optimal