Elliptic curve isogeny class with LMFDB label 81600.hn (Cremona label 81600ht)

• Label: 81600.hn
• Number of curves: $4$
• Conductor: $81600$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 81600.hn have rank \(1\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 + 7 T^{2}\)	1.7.a
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 + 8 T + 23 T^{2}\)	1.23.i
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 81600.hn do not have complex multiplication.

Modular form 81600.2.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 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 81600.hn

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
81600.hn1	81600ht4	\([0, 1, 0, -400033, 28340063]\)	\(6913728144004/3658971285\)	\(3746786595840000000\)	\([2]\)	\(1179648\)	\(2.2555\)
81600.hn2	81600ht2	\([0, 1, 0, -230033, -42209937]\)	\(5258429611216/47403225\)	\(12135225600000000\)	\([2, 2]\)	\(589824\)	\(1.9089\)
81600.hn3	81600ht1	\([0, 1, 0, -229533, -42403437]\)	\(83587439220736/6885\)	\(110160000000\)	\([2]\)	\(294912\)	\(1.5623\)	\(\Gamma_0(N)\)-optimal
81600.hn4	81600ht3	\([0, 1, 0, -68033, -100367937]\)	\(-34008619684/4228250625\)	\(-4329728640000000000\)	\([2]\)	\(1179648\)	\(2.2555\)