Elliptic curve isogeny class with Cremona label 20592bt (LMFDB label 20592.bn)

• Label: 20592bt
• Number of curves: $4$
• Conductor: $20592$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 20592bt have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(11\)	\(1 - T\)
\(13\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - 2 T + 5 T^{2}\)	1.5.ac
\(7\)	\( 1 - 2 T + 7 T^{2}\)	1.7.ac
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 + 2 T + 19 T^{2}\)	1.19.c
\(23\)	\( 1 + 8 T + 23 T^{2}\)	1.23.i
\(29\)	\( 1 - 4 T + 29 T^{2}\)	1.29.ae
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 20592bt do not have complex multiplication.

Modular form 20592.2.a.bt

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 20592bt

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
20592.bn4	20592bt1	\([0, 0, 0, -22179, 1478050]\)	\(-404075127457/82223856\)	\(-245519118434304\)	\([2]\)	\(55296\)	\(1.4836\)	\(\Gamma_0(N)\)-optimal
20592.bn3	20592bt2	\([0, 0, 0, -370659, 86855650]\)	\(1886079023633377/59629284\)	\(178052087955456\)	\([2, 2]\)	\(110592\)	\(1.8301\)
20592.bn2	20592bt3	\([0, 0, 0, -386499, 79027522]\)	\(2138362647385537/333926700822\)	\(997099785827278848\)	\([2]\)	\(221184\)	\(2.1767\)
20592.bn1	20592bt4	\([0, 0, 0, -5930499, 5558850178]\)	\(7725203825376001537/7722\)	\(23057768448\)	\([2]\)	\(221184\)	\(2.1767\)