Elliptic curve isogeny class with Cremona label 228800de (LMFDB label 228800.fl)

• Label: 228800de
• Number of curves: $4$
• Conductor: $228800$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 228800de have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(5\)	\(1\)
\(11\)	\(1 + T\)
\(13\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + 3 T^{2}\)	1.3.a
\(7\)	\( 1 + 7 T^{2}\)	1.7.a
\(17\)	\( 1 - 5 T + 17 T^{2}\)	1.17.af
\(19\)	\( 1 + 3 T + 19 T^{2}\)	1.19.d
\(23\)	\( 1 - 6 T + 23 T^{2}\)	1.23.ag
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 228800de do not have complex multiplication.

Modular form 228800.2.a.de

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 228800de

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
228800.fl4	228800de1	\([0, -1, 0, 166367, 499137]\)	\(124326214271/71980480\)	\(-294832046080000000\)	\([2]\)	\(3538944\)	\(2.0416\)	\(\Gamma_0(N)\)-optimal
228800.fl3	228800de2	\([0, -1, 0, -665633, 4659137]\)	\(7962857630209/4606058600\)	\(18866416025600000000\)	\([2]\)	\(7077888\)	\(2.3881\)
228800.fl2	228800de3	\([0, -1, 0, -2297633, 1432083137]\)	\(-327495950129089/26547449500\)	\(-108738353152000000000\)	\([2]\)	\(10616832\)	\(2.5909\)
228800.fl1	228800de4	\([0, -1, 0, -37449633, 88222371137]\)	\(1418098748958579169/8307406250\)	\(34027136000000000000\)	\([2]\)	\(21233664\)	\(2.9374\)