Elliptic curve isogeny class with LMFDB label 3024.b (Cremona label 3024l)

• Label: 3024.b
• Number of curves: $1$
• Conductor: $3024$
• CM: no
• Rank: $1$

Rank

The elliptic curve 3024.b1 has rank \(1\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 4 T + 5 T^{2}\)	1.5.e
\(11\)	\( 1 - 4 T + 11 T^{2}\)	1.11.ae
\(13\)	\( 1 + T + 13 T^{2}\)	1.13.b
\(17\)	\( 1 + 3 T + 17 T^{2}\)	1.17.d
\(19\)	\( 1 + 2 T + 19 T^{2}\)	1.19.c
\(23\)	\( 1 + 3 T + 23 T^{2}\)	1.23.d
\(29\)	\( 1 - 9 T + 29 T^{2}\)	1.29.aj
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 3024.b do not have complex multiplication.

Modular form 3024.2.a.b

Elliptic curves in class 3024.b

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
3024.b1	3024l1	\([0, 0, 0, -27, 810]\)	\(-54/7\)	\(-282175488\)	\([]\)	\(1440\)	\(0.30094\)	\(\Gamma_0(N)\)-optimal