Elliptic curve isogeny class with LMFDB label 1200.a (Cremona label 1200n)

• Label: 1200.a
• Number of curves: $2$
• Conductor: $1200$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 1200.a have rank \(1\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 + 4 T + 7 T^{2}\)	1.7.e
\(11\)	\( 1 - 4 T + 11 T^{2}\)	1.11.ae
\(13\)	\( 1 + 13 T^{2}\)	1.13.a
\(17\)	\( 1 - 4 T + 17 T^{2}\)	1.17.ae
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 1200.a do not have complex multiplication.

Modular form 1200.2.a.a

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 1200.a

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
1200.a1	1200n1	\([0, -1, 0, -333, -2088]\)	\(131072/9\)	\(281250000\)	\([2]\)	\(480\)	\(0.36947\)	\(\Gamma_0(N)\)-optimal
1200.a2	1200n2	\([0, -1, 0, 292, -9588]\)	\(5488/81\)	\(-40500000000\)	\([2]\)	\(960\)	\(0.71604\)