Elliptic curve isogeny class with LMFDB label 26400.bt (Cremona label 26400ca)

• Label: 26400.bt
• Number of curves: $4$
• Conductor: $26400$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 26400.bt have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 - T\)
\(5\)	\(1\)
\(11\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 + 7 T^{2}\)	1.7.a
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 - 6 T + 17 T^{2}\)	1.17.ag
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
\(29\)	\( 1 - 10 T + 29 T^{2}\)	1.29.ak
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 26400.bt do not have complex multiplication.

Modular form 26400.2.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 LMFDB numbering.

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 26400.bt

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
26400.bt1	26400ca4	\([0, 1, 0, -221888008, 1272106648988]\)	\(151020262560470148771848/35809491031875\)	\(286475928255000000000\)	\([2]\)	\(2949120\)	\(3.3041\)
26400.bt2	26400ca3	\([0, 1, 0, -27395633, -24685819137]\)	\(35529391776305786176/16450653076171875\)	\(1052841796875000000000000\)	\([2]\)	\(2949120\)	\(3.3041\)
26400.bt3	26400ca1	\([0, 1, 0, -13919258, 19718836488]\)	\(298244193811346574784/4540317078515625\)	\(4540317078515625000000\)	\([2, 2]\)	\(1474560\)	\(2.9575\)	\(\Gamma_0(N)\)-optimal
26400.bt4	26400ca2	\([0, 1, 0, -1263008, 54245086488]\)	\(-27851742625371848/158882936571500625\)	\(-1271063492572005000000000\)	\([2]\)	\(2949120\)	\(3.3041\)