Elliptic curve isogeny class with Cremona label 8820r (LMFDB label 8820.a)

• Label: 8820r
• Number of curves: $2$
• Conductor: $8820$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 8820r have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(5\)	\(1 - T\)
\(7\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 + 3 T + 11 T^{2}\)	1.11.d
\(13\)	\( 1 - T + 13 T^{2}\)	1.13.ab
\(17\)	\( 1 + 3 T + 17 T^{2}\)	1.17.d
\(19\)	\( 1 + 2 T + 19 T^{2}\)	1.19.c
\(23\)	\( 1 - 6 T + 23 T^{2}\)	1.23.ag
\(29\)	\( 1 - 9 T + 29 T^{2}\)	1.29.aj
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 8820r do not have complex multiplication.

Modular form 8820.2.a.r

Isogeny matrix

The \((i,j)\)-th 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, and the \( \Gamma_0(N) \)-optimal curve is highlighted in blue.

Elliptic curves in class 8820r

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
8820.a1	8820r1	\([0, 0, 0, -439383, 112169918]\)	\(-177953104/125\)	\(-6589582608672000\)	\([]\)	\(90720\)	\(1.9716\)	\(\Gamma_0(N)\)-optimal
8820.a2	8820r2	\([0, 0, 0, 424977, 476411222]\)	\(161017136/1953125\)	\(-102962228260500000000\)	\([]\)	\(272160\)	\(2.5210\)