Elliptic curve isogeny class with LMFDB label 308550.kd (Cremona label 308550kd)

• Label: 308550.kd
• Number of curves: $4$
• Conductor: $308550$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 308550.kd have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(3\)	\(1 - T\)
\(5\)	\(1\)
\(11\)	\(1\)
\(17\)	\(1 - T\)

Good L-factors:

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

See L-function page for more information

Complex multiplication

The elliptic curves in class 308550.kd do not have complex multiplication.

Modular form 308550.2.a.kd

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 LMFDB 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 LMFDB labels.

Elliptic curves in class 308550.kd

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
308550.kd1	308550kd3	\([1, 0, 0, -5859488, 5059263342]\)	\(803760366578833/65593817586\)	\(1815678891819871031250\)	\([2]\)	\(23592960\)	\(2.8219\)
308550.kd2	308550kd2	\([1, 0, 0, -1231238, -434469408]\)	\(7457162887153/1370924676\)	\(37948073280300562500\)	\([2, 2]\)	\(11796480\)	\(2.4754\)
308550.kd3	308550kd1	\([1, 0, 0, -1170738, -487648908]\)	\(6411014266033/296208\)	\(8199227198250000\)	\([2]\)	\(5898240\)	\(2.1288\)	\(\Gamma_0(N)\)-optimal
308550.kd4	308550kd4	\([1, 0, 0, 2429012, -2524472158]\)	\(57258048889007/132611470002\)	\(-3670770443878330031250\)	\([2]\)	\(23592960\)	\(2.8219\)