Elliptic curve isogeny class with Cremona label 201600hn (LMFDB label 201600.iw)

• Label: 201600hn
• Number of curves: $2$
• Conductor: $201600$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 201600hn 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 \(\mathbb{F}_p\)
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 201600hn do not have complex multiplication.

Modular form 201600.2.a.hn

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 201600hn

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
201600.iw1	201600hn1	\([0, 0, 0, -3450, 33500]\)	\(1557376/735\)	\(2143260000000\)	\([2]\)	\(245760\)	\(1.0603\)	\(\Gamma_0(N)\)-optimal
201600.iw2	201600hn2	\([0, 0, 0, 12300, 254000]\)	\(2205472/1575\)	\(-146966400000000\)	\([2]\)	\(491520\)	\(1.4069\)