Elliptic curve isogeny class with Cremona label 59584cl (LMFDB label 59584.z)

• Label: 59584cl
• Number of curves: $3$
• Conductor: $59584$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 59584cl have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(7\)	\(1\)
\(19\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 - 2 T + 3 T^{2}\)	1.3.ac
\(5\)	\( 1 + T + 5 T^{2}\)	1.5.b
\(11\)	\( 1 + 3 T + 11 T^{2}\)	1.11.d
\(13\)	\( 1 + 4 T + 13 T^{2}\)	1.13.e
\(17\)	\( 1 + 5 T + 17 T^{2}\)	1.17.f
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 59584cl do not have complex multiplication.

Modular form 59584.2.a.cl

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.

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 59584cl

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
59584.z2	59584cl1	\([0, -1, 0, -48673, 4150721]\)	\(-413493625/152\)	\(-4687828877312\)	\([]\)	\(145152\)	\(1.3992\)	\(\Gamma_0(N)\)-optimal
59584.z3	59584cl2	\([0, -1, 0, 29727, 15700609]\)	\(94196375/3511808\)	\(-108307598381416448\)	\([]\)	\(435456\)	\(1.9485\)
59584.z1	59584cl3	\([0, -1, 0, -268193, -429928127]\)	\(-69173457625/2550136832\)	\(-78648717645700923392\)	\([]\)	\(1306368\)	\(2.4978\)