Elliptic curve isogeny class with Cremona label 8820z (LMFDB label 8820.t)

• Label: 8820z
• Number of curves: $2$
• Conductor: $8820$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 8820z have rank \(1\).

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 \(\mathbb{F}_p\)
\(11\)	\( 1 - 4 T + 11 T^{2}\)	1.11.ae
\(13\)	\( 1 + 13 T^{2}\)	1.13.a
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 - 6 T + 19 T^{2}\)	1.19.ag
\(23\)	\( 1 - 6 T + 23 T^{2}\)	1.23.ag
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 8820.2.a.z

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.

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

Isogeny graph

The vertices are labelled with Cremona labels, and the \( \Gamma_0(N) \)-optimal curve is highlighted in blue.

Elliptic curves in class 8820z

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
8820.t2	8820z1	\([0, 0, 0, -13692, 531601]\)	\(70954958848/10546875\)	\(42195431250000\)	\([2]\)	\(18432\)	\(1.3390\)	\(\Gamma_0(N)\)-optimal
8820.t1	8820z2	\([0, 0, 0, -210567, 37189726]\)	\(16129950234928/455625\)	\(29165482080000\)	\([2]\)	\(36864\)	\(1.6855\)