Elliptic curve isogeny class with Cremona label 82810bu (LMFDB label 82810.cb)

• Label: 82810bu
• Number of curves: $2$
• Conductor: $82810$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 82810bu 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 \(\mathbb{F}_p\)
\(3\)	\( 1 + T + 3 T^{2}\)	1.3.b
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(17\)	\( 1 - 3 T + 17 T^{2}\)	1.17.ad
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 + 6 T + 23 T^{2}\)	1.23.g
\(29\)	\( 1 + 3 T + 29 T^{2}\)	1.29.d
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 82810.2.a.bu

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.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 82810bu

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
82810.cb2	82810bu1	\([1, -1, 1, -42958, -5574019]\)	\(-2609064081/2500000\)	\(-8400432722500000\)	\([]\)	\(554400\)	\(1.7518\)	\(\Gamma_0(N)\)-optimal
82810.cb1	82810bu2	\([1, -1, 1, -3769408, 3045726051]\)	\(-1762712152495281/171798691840\)	\(-577273341046171893760\)	\([]\)	\(3880800\)	\(2.7247\)