Elliptic curve isogeny class with Cremona label 82800co (LMFDB label 82800.eu)

• Label: 82800co
• Number of curves: $2$
• Conductor: $82800$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 82800co have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(5\)	\(1\)
\(23\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 + T + 7 T^{2}\)	1.7.b
\(11\)	\( 1 - 3 T + 11 T^{2}\)	1.11.ad
\(13\)	\( 1 - T + 13 T^{2}\)	1.13.ab
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 - T + 19 T^{2}\)	1.19.ab
\(29\)	\( 1 - 3 T + 29 T^{2}\)	1.29.ad
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 82800co do not have complex multiplication.

Modular form 82800.2.a.co

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 82800co

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
82800.eu2	82800co1	\([0, 0, 0, -5400, 151875]\)	\(3538944/23\)	\(113177250000\)	\([2]\)	\(73728\)	\(0.95710\)	\(\Gamma_0(N)\)-optimal
82800.eu1	82800co2	\([0, 0, 0, -8775, -60750]\)	\(949104/529\)	\(41649228000000\)	\([2]\)	\(147456\)	\(1.3037\)