Elliptic curve isogeny class with LMFDB label 12544.c (Cremona label 12544o)

• Label: 12544.c
• Number of curves: $2$
• Conductor: $12544$
• CM: \(\Q(\sqrt{-2}) \)
• Rank: $1$

Rank

The elliptic curves in class 12544.c have rank \(1\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + 2 T + 3 T^{2}\)	1.3.c
\(5\)	\( 1 + 5 T^{2}\)	1.5.a
\(11\)	\( 1 - 6 T + 11 T^{2}\)	1.11.ag
\(13\)	\( 1 + 13 T^{2}\)	1.13.a
\(17\)	\( 1 - 6 T + 17 T^{2}\)	1.17.ag
\(19\)	\( 1 + 2 T + 19 T^{2}\)	1.19.c
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

Each elliptic curve in class 12544.c has complex multiplication by an order in the imaginary quadratic field \(\Q(\sqrt{-2}) \).

Modular form 12544.2.a.c

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 LMFDB numbering.

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

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 12544.c

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality	CM discriminant
12544.c1	12544o2	\([0, 1, 0, -653, -5909]\)	\(8000\)	\(3855122432\)	\([2]\)	\(6144\)	\(0.56898\)		\(-8\)
12544.c2	12544o1	\([0, 1, 0, -163, 657]\)	\(8000\)	\(60236288\)	\([2]\)	\(3072\)	\(0.22241\)	\(\Gamma_0(N)\)-optimal	\(-8\)