Elliptic curve isogeny class with Cremona label 30345z (LMFDB label 30345.b)

• Label: 30345z
• Number of curves: $1$
• Conductor: $30345$
• CM: no
• Rank: $1$

Rank

The elliptic curve 30345z1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(3\)	\(1 - T\)
\(5\)	\(1 + T\)
\(7\)	\(1 + T\)
\(17\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(2\)	\( 1 - T + 2 T^{2}\)	1.2.ab
\(11\)	\( 1 + 4 T + 11 T^{2}\)	1.11.e
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 30345z do not have complex multiplication.

Modular form 30345.2.a.z

Elliptic curves in class 30345z

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
30345.b1	30345z1	\([0, 1, 1, -266, 1580]\)	\(7229403136/19845\)	\(5735205\)	\([]\)	\(12672\)	\(0.17002\)	\(\Gamma_0(N)\)-optimal