Elliptic curve isogeny class with Cremona label 12600cc (LMFDB label 12600.ci)

• Label: 12600cc
• Number of curves: $4$
• Conductor: $12600$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 12600cc have rank \(0\).

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 \(\mathbb{F}_p\)
\(11\)	\( 1 - 2 T + 11 T^{2}\)	1.11.ac
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
\(29\)	\( 1 + 10 T + 29 T^{2}\)	1.29.k
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 12600.2.a.cc

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 12600cc

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
12600.ci4	12600cc1	\([0, 0, 0, 225, -6750]\)	\(432/7\)	\(-20412000000\)	\([2]\)	\(8192\)	\(0.65884\)	\(\Gamma_0(N)\)-optimal
12600.ci3	12600cc2	\([0, 0, 0, -4275, -101250]\)	\(740772/49\)	\(571536000000\)	\([2, 2]\)	\(16384\)	\(1.0054\)
12600.ci1	12600cc3	\([0, 0, 0, -67275, -6716250]\)	\(1443468546/7\)	\(163296000000\)	\([2]\)	\(32768\)	\(1.3520\)
12600.ci2	12600cc4	\([0, 0, 0, -13275, 465750]\)	\(11090466/2401\)	\(56010528000000\)	\([2]\)	\(32768\)	\(1.3520\)