Elliptic curve isogeny class with Cremona label 12144bk (LMFDB label 12144.bi)

• Label: 12144bk
• Number of curves: $2$
• Conductor: $12144$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 12144bk have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 - T\)
\(11\)	\(1 - T\)
\(23\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - T + 5 T^{2}\)	1.5.ab
\(7\)	\( 1 + T + 7 T^{2}\)	1.7.b
\(13\)	\( 1 + 5 T + 13 T^{2}\)	1.13.f
\(17\)	\( 1 - 3 T + 17 T^{2}\)	1.17.ad
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(29\)	\( 1 + 3 T + 29 T^{2}\)	1.29.d
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 12144bk do not have complex multiplication.

Modular form 12144.2.a.bk

Isogeny matrix

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 12144bk

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
12144.bi2	12144bk1	\([0, 1, 0, 672, 4212]\)	\(8181353375/6412032\)	\(-26263683072\)	\([2]\)	\(9216\)	\(0.68727\)	\(\Gamma_0(N)\)-optimal
12144.bi1	12144bk2	\([0, 1, 0, -3168, 33396]\)	\(858729462625/371764272\)	\(1522746458112\)	\([2]\)	\(18432\)	\(1.0338\)