Elliptic curve isogeny class with LMFDB label 6912.o (Cremona label 6912a)

• Label: 6912.o
• Number of curves: $1$
• Conductor: $6912$
• CM: no
• Rank: $1$

Rank

The elliptic curve 6912.o1 has rank \(1\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - T + 5 T^{2}\)	1.5.ab
\(7\)	\( 1 - 3 T + 7 T^{2}\)	1.7.ad
\(11\)	\( 1 - 3 T + 11 T^{2}\)	1.11.ad
\(13\)	\( 1 + 4 T + 13 T^{2}\)	1.13.e
\(17\)	\( 1 + 4 T + 17 T^{2}\)	1.17.e
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 6912.o do not have complex multiplication.

Modular form 6912.2.a.o

Elliptic curves in class 6912.o

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
6912.o1	6912a1	\([0, 0, 0, -552, 4992]\)	\(-21024576\)	\(-884736\)	\([]\)	\(1536\)	\(0.21474\)	\(\Gamma_0(N)\)-optimal