Elliptic curve isogeny class with Cremona label 338800el (LMFDB label 338800.el)

• Label: 338800el
• Number of curves: $4$
• Conductor: $338800$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 338800el have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(5\)	\(1\)
\(7\)	\(1 - T\)
\(11\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + 3 T^{2}\)	1.3.a
\(13\)	\( 1 + 6 T + 13 T^{2}\)	1.13.g
\(17\)	\( 1 - 6 T + 17 T^{2}\)	1.17.ag
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 + 8 T + 23 T^{2}\)	1.23.i
\(29\)	\( 1 - 10 T + 29 T^{2}\)	1.29.ak
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 338800el do not have complex multiplication.

Modular form 338800.2.a.el

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 338800el

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
338800.el4	338800el1	\([0, 0, 0, -1775675, 1225518250]\)	\(-5461074081/2562175\)	\(-290499155531200000000\)	\([2]\)	\(11796480\)	\(2.6326\)	\(\Gamma_0(N)\)-optimal
338800.el3	338800el2	\([0, 0, 0, -31057675, 66612224250]\)	\(29220958012401/3705625\)	\(420143406760000000000\)	\([2, 2]\)	\(23592960\)	\(2.9791\)
338800.el1	338800el3	\([0, 0, 0, -496907675, 4263454874250]\)	\(119678115308998401/1925\)	\(218256315200000000\)	\([2]\)	\(47185920\)	\(3.3257\)
338800.el2	338800el4	\([0, 0, 0, -33719675, 54518758250]\)	\(37397086385121/10316796875\)	\(1169717439275000000000000\)	\([2]\)	\(47185920\)	\(3.3257\)