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

• Label: 1200a
• Number of curves: $6$
• Conductor: $1200$
• CM: no
• Rank: $1$

Rank

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

Modular form 1200.2.a.a

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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 1200a

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
1200.d5	1200a1	\([0, -1, 0, 17, -38]\)	\(2048/3\)	\(-750000\)	\([2]\)	\(128\)	\(-0.18721\)	\(\Gamma_0(N)\)-optimal
1200.d4	1200a2	\([0, -1, 0, -108, -288]\)	\(35152/9\)	\(36000000\)	\([2, 2]\)	\(256\)	\(0.15937\)
1200.d2	1200a3	\([0, -1, 0, -1608, -24288]\)	\(28756228/3\)	\(48000000\)	\([2]\)	\(512\)	\(0.50594\)
1200.d3	1200a4	\([0, -1, 0, -608, 5712]\)	\(1556068/81\)	\(1296000000\)	\([2, 2]\)	\(512\)	\(0.50594\)
1200.d1	1200a5	\([0, -1, 0, -9608, 365712]\)	\(3065617154/9\)	\(288000000\)	\([2]\)	\(1024\)	\(0.85251\)
1200.d6	1200a6	\([0, -1, 0, 392, 21712]\)	\(207646/6561\)	\(-209952000000\)	\([2]\)	\(1024\)	\(0.85251\)