Elliptic curve isogeny class with Cremona label 226800dw (LMFDB label 226800.ho)

• Label: 226800dw
• Number of curves: $2$
• Conductor: $226800$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 226800dw have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(5\)	\(1\)
\(7\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 - 5 T + 11 T^{2}\)	1.11.af
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 + 4 T + 17 T^{2}\)	1.17.e
\(19\)	\( 1 + 2 T + 19 T^{2}\)	1.19.c
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 226800dw do not have complex multiplication.

Modular form 226800.2.a.dw

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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 226800dw

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
226800.ho2	226800dw1	\([0, 0, 0, 313125, 50106250]\)	\(1047929175/941192\)	\(-3049462080000000000\)	\([]\)	\(2799360\)	\(2.2342\)	\(\Gamma_0(N)\)-optimal
226800.ho1	226800dw2	\([0, 0, 0, -7036875, 7270256250]\)	\(-1812792825/25088\)	\(-533311672320000000000\)	\([]\)	\(8398080\)	\(2.7835\)