Elliptic curve isogeny class with LMFDB label 30912.ck (Cremona label 30912x)

• Label: 30912.ck
• Number of curves: $1$
• Conductor: $30912$
• CM: no
• Rank: $1$

Rank

The elliptic curve 30912.ck1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 - T\)
\(7\)	\(1 + T\)
\(23\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - 3 T + 5 T^{2}\)	1.5.ad
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 - T + 13 T^{2}\)	1.13.ab
\(17\)	\( 1 + 4 T + 17 T^{2}\)	1.17.e
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(29\)	\( 1 + 5 T + 29 T^{2}\)	1.29.f
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 30912.ck do not have complex multiplication.

Modular form 30912.2.a.ck

Elliptic curves in class 30912.ck

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
30912.ck1	30912x1	\([0, 1, 0, -1569, -34497]\)	\(-3261064466/1917027\)	\(-251268562944\)	\([]\)	\(38400\)	\(0.89004\)	\(\Gamma_0(N)\)-optimal