Elliptic curve isogeny class with Cremona label 59290dz (LMFDB label 59290.cp)

• Label: 59290dz
• Number of curves: $2$
• Conductor: $59290$
• CM: no
• Rank: $2$

Rank

The elliptic curves in class 59290dz have rank \(2\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(5\)	\(1 - T\)
\(7\)	\(1\)
\(11\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 - T + 3 T^{2}\)	1.3.ab
\(13\)	\( 1 + 4 T + 13 T^{2}\)	1.13.e
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(19\)	\( 1 - 2 T + 19 T^{2}\)	1.19.ac
\(23\)	\( 1 + 9 T + 23 T^{2}\)	1.23.j
\(29\)	\( 1 + 3 T + 29 T^{2}\)	1.29.d
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 59290dz do not have complex multiplication.

Modular form 59290.2.a.dz

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 59290dz

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
59290.cp2	59290dz1	\([1, 0, 0, -10095, 580537]\)	\(-726572699/512000\)	\(-80174499328000\)	\([2]\)	\(276480\)	\(1.3679\)	\(\Gamma_0(N)\)-optimal
59290.cp1	59290dz2	\([1, 0, 0, -182575, 30005625]\)	\(4298149261979/1000000\)	\(156590819000000\)	\([2]\)	\(552960\)	\(1.7145\)