Elliptic curve isogeny class with Cremona label 12600ba (LMFDB label 12600.k)

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

Rank

The elliptic curves in class 12600ba 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 \(\mathbb{F}_p\)
\(11\)	\( 1 - 4 T + 11 T^{2}\)	1.11.ae
\(13\)	\( 1 - T + 13 T^{2}\)	1.13.ab
\(17\)	\( 1 - 3 T + 17 T^{2}\)	1.17.ad
\(19\)	\( 1 + 6 T + 19 T^{2}\)	1.19.g
\(23\)	\( 1 + 3 T + 23 T^{2}\)	1.23.d
\(29\)	\( 1 + 3 T + 29 T^{2}\)	1.29.d
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 12600.2.a.ba

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.

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

Isogeny graph

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

Elliptic curves in class 12600ba

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
12600.k1	12600ba1	\([0, 0, 0, -138855, 19915450]\)	\(12692020761488/9261\)	\(216040608000\)	\([2]\)	\(36864\)	\(1.4860\)	\(\Gamma_0(N)\)-optimal
12600.k2	12600ba2	\([0, 0, 0, -137955, 20186350]\)	\(-3111705953492/85766121\)	\(-8003008282752000\)	\([2]\)	\(73728\)	\(1.8326\)