Elliptic curve isogeny class with LMFDB label 12600.j (Cremona label 12600bb)

• Label: 12600.j
• Number of curves: $2$
• Conductor: $12600$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 12600.j 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 \(\mathbb{F}_p\)
\(11\)	\( 1 + 2 T + 11 T^{2}\)	1.11.c
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 + 6 T + 19 T^{2}\)	1.19.g
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 12600.2.a.j

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 LMFDB numbering.

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

Isogeny graph

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

Elliptic curves in class 12600.j

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
12600.j1	12600bb1	\([0, 0, 0, -6375, -143750]\)	\(78608/21\)	\(7654500000000\)	\([2]\)	\(20480\)	\(1.1805\)	\(\Gamma_0(N)\)-optimal
12600.j2	12600bb2	\([0, 0, 0, 16125, -931250]\)	\(318028/441\)	\(-642978000000000\)	\([2]\)	\(40960\)	\(1.5271\)