Elliptic curve isogeny class with Cremona label 26640bz (LMFDB label 26640.bu)

• Label: 26640bz
• Number of curves: $2$
• Conductor: $26640$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 26640bz have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(5\)	\(1 - T\)
\(37\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 - 3 T + 7 T^{2}\)	1.7.ad
\(11\)	\( 1 - 5 T + 11 T^{2}\)	1.11.af
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 + 4 T + 17 T^{2}\)	1.17.e
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 - 6 T + 23 T^{2}\)	1.23.ag
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 26640bz do not have complex multiplication.

Modular form 26640.2.a.bz

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 26640bz

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
26640.bu2	26640bz1	\([0, 0, 0, -12009027, -21372032446]\)	\(-64144540676215729729/28962038218752000\)	\(-86480182728581971968000\)	\([]\)	\(1520640\)	\(3.1079\)	\(\Gamma_0(N)\)-optimal
26640.bu1	26640bz2	\([0, 0, 0, -1060421187, -13291246835134]\)	\(-44164307457093068844199489/1823508000000000\)	\(-5444965711872000000000\)	\([]\)	\(4561920\)	\(3.6572\)