Elliptic curve isogeny class with Cremona label 12600bs (LMFDB label 12600.o)

• Label: 12600bs
• Number of curves: $4$
• Conductor: $12600$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 12600bs have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(5\)	\(1\)
\(7\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 + T + 11 T^{2}\)	1.11.b
\(13\)	\( 1 + 4 T + 13 T^{2}\)	1.13.e
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 - 6 T + 19 T^{2}\)	1.19.ag
\(23\)	\( 1 - 3 T + 23 T^{2}\)	1.23.ad
\(29\)	\( 1 - 3 T + 29 T^{2}\)	1.29.ad
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 12600bs do not have complex multiplication.

Modular form 12600.2.a.bs

Isogeny matrix

The \((i,j)\)-th 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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels, and the \( \Gamma_0(N) \)-optimal curve is highlighted in blue.

Elliptic curves in class 12600bs

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
12600.o3	12600bs1	\([0, 0, 0, -8175, 283250]\)	\(20720464/105\)	\(306180000000\)	\([4]\)	\(12288\)	\(1.0505\)	\(\Gamma_0(N)\)-optimal
12600.o2	12600bs2	\([0, 0, 0, -12675, -63250]\)	\(19307236/11025\)	\(128595600000000\)	\([2, 2]\)	\(24576\)	\(1.3971\)
12600.o1	12600bs3	\([0, 0, 0, -147675, -21798250]\)	\(15267472418/36015\)	\(840157920000000\)	\([2]\)	\(49152\)	\(1.7437\)
12600.o4	12600bs4	\([0, 0, 0, 50325, -504250]\)	\(604223422/354375\)	\(-8266860000000000\)	\([2]\)	\(49152\)	\(1.7437\)