Elliptic curve isogeny class with LMFDB label 82810.ca (Cremona label 82810bv)

• Label: 82810.ca
• Number of curves: $4$
• Conductor: $82810$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 82810.ca have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(5\)	\(1 + T\)
\(7\)	\(1\)
\(13\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + 3 T^{2}\)	1.3.a
\(11\)	\( 1 + 4 T + 11 T^{2}\)	1.11.e
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 - 8 T + 23 T^{2}\)	1.23.ai
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 82810.ca do not have complex multiplication.

Modular form 82810.2.a.ca

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 82810.ca

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
82810.ca1	82810bv4	\([1, -1, 1, -902961793, 10443559324657]\)	\(143378317900125424089/4976562500000\)	\(2826036824610289062500000\)	\([2]\)	\(30965760\)	\(3.7824\)
82810.ca2	82810bv2	\([1, -1, 1, -58962273, 147777980081]\)	\(39920686684059609/6492304000000\)	\(3686779816502792464000000\)	\([2, 2]\)	\(15482880\)	\(3.4358\)
82810.ca3	82810bv1	\([1, -1, 1, -16563553, -23733322063]\)	\(884984855328729/83492864000\)	\(47413030230440935424000\)	\([2]\)	\(7741440\)	\(3.0892\)	\(\Gamma_0(N)\)-optimal
82810.ca4	82810bv3	\([1, -1, 1, 106657727, 828211188081]\)	\(236293804275620391/658593925444000\)	\(-373995239840630398831204000\)	\([2]\)	\(30965760\)	\(3.7824\)